{"id":6673,"date":"2025-12-24T17:19:15","date_gmt":"2025-12-24T08:19:15","guid":{"rendered":"https:\/\/math-travel.com\/?p=6673"},"modified":"2026-02-11T16:29:18","modified_gmt":"2026-02-11T07:29:18","slug":"addition-theorem","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/","title":{"rendered":"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac"},"content":{"rendered":"\n

\u300c\u52a0\u6cd5\u5b9a\u7406\u3063\u3066\u306a\u3093\u3060\u3063\u3051\uff1f\u300d<\/span>
\u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u77e5\u308a\u305f\u3044\u300d<\/span>
\u4eca\u56de\u306f\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u52a0\u6cd5\u5b9a\u7406\u3063\u3066\u306a\u3093\u3060\u3063\u3051\u2026\uff1f<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u306a\u304b\u3067\u3082\u52a0\u6cd5\u5b9a\u7406\u306f\u91cd\u8981\u306a\u516c\u5f0f\u306e1\u3064<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406<\/span><\/div>
\n

\\begin{eqnarray}
\\sin(\\alpha+\\beta)&=&\\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta\\\\
\\sin(\\alpha-\\beta)&=&\\sin \\alpha \\cos \\beta-\\cos \\alpha \\sin \\beta\\\\
\\cos(\\alpha+\\beta)&=&\\cos \\alpha \\cos \\beta-\\sin \\alpha \\sin \\beta\\\\
\\cos(\\alpha-\\beta)&=&\\cos \\alpha \\cos \\beta+\\sin \\alpha \\sin \\beta\\\\
\\displaystyle \\tan(\\alpha+\\beta)&=&\\frac{\\tan \\alpha+\\tan \\beta}{1-\\tan \\alpha \\tan \\beta}\\\\
\\displaystyle \\tan(\\alpha-\\beta)&=&\\frac{\\tan \\alpha -\\tan \\beta}{1+\\tan \\alpha \\tan \\beta}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001\\(\\sin 105^\\circ\\)\u3084\\(\\cos 15^\\circ\\)\u306a\u3069\u306e\u4e09\u89d2\u6bd4\u3092<\/span>\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u5fb9\u5e95\u89e3\u8aac<\/span>\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

\u5927\u4e8b\u306a\u3053\u3068\u304c\u8a70\u307e\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u52a0\u6cd5\u5b9a\u7406\u304c\u82e6\u624b\u306a\u65b9\u306f\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

\n
    \n
  1. \u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f<\/a><\/li>\n\n\n\n
  2. \u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9<\/a><\/li>\n\n\n\n
  3. \u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e<\/a><\/li>\n\n\n\n
  4. 2\u500d\u89d2\u306e\u516c\u5f0f<\/a><\/li>\n\n\n\n
  5. \u534a\u89d2\u306e\u516c\u5f0f<\/a><\/li>\n\n\n\n
  6. \u7df4\u7fd2\u554f\u984c<\/a><\/li>\n\n\n\n
  7. \u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u3000\u307e\u3068\u3081<\/a><\/li>\n<\/ol>\n<\/div><\/div>\n\n\n
    \"\"\u30b7\u30fc\u30bf<\/span><\/div>
    \n

    \u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001
    \u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

    \u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f<\/h2>\n\n\n\n

    \u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

    \u52a0\u6cd5\u5b9a\u7406<\/span><\/div>
    \n

    \\begin{eqnarray}
    \\sin(\\alpha+\\beta)&=&\\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta\\\\
    \\sin(\\alpha-\\beta)&=&\\sin \\alpha \\cos \\beta-\\cos \\alpha \\sin \\beta\\\\
    \\cos(\\alpha+\\beta)&=&\\cos \\alpha \\cos \\beta-\\sin \\alpha \\sin \\beta\\\\
    \\cos(\\alpha-\\beta)&=&\\cos \\alpha \\cos \\beta+\\sin \\alpha \\sin \\beta\\\\
    \\displaystyle \\tan(\\alpha+\\beta)&=&\\frac{\\tan \\alpha+\\tan \\beta}{1-\\tan \\alpha \\tan \\beta}\\\\
    \\displaystyle \\tan(\\alpha-\\beta)&=&\\frac{\\tan \\alpha -\\tan \\beta}{1+\\tan \\alpha \\tan \\beta}
    \\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

    \u899a\u3048\u306b\u304f\u3044\u516c\u5f0f\u306a\u306e\u3067\u3001\u5f8c\u307b\u3069\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n

    \"\"\u30b7\u30fc\u30bf<\/span><\/div>
    \n

    \u305d\u308c\u305e\u308c\u306e\u516c\u5f0f\u3092\u4f8b\u984c\u3092\u4ea4\u3048\u3066\u89e3\u8aac\u3059\u308b\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

    \\(\\sin\\)\u306e\u52a0\u6cd5\u5b9a\u7406<\/h3>\n\n\n\n

    \\(\\sin\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

    \u52a0\u6cd5\u5b9a\u7406<\/span><\/div>
    \n

    \\begin{eqnarray}
    \\sin(\\alpha+\\beta)=\\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta\\\\
    \\sin(\\alpha-\\beta)=\\sin \\alpha \\cos \\beta-\\cos \\alpha \\sin \\beta
    \\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

    \\(\\sin\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

    \\begin{eqnarray}
    \\sin 105^\\circ &=& \\sin(45^\\circ + 60^\\circ)\\\\
    &=&\\sin 45^\\circ \\cos 60^\\circ+\\cos 45^\\circ \\sin 60^\\circ\\\\
    \\displaystyle &=&\\frac{1}{2 \\sqrt{2}}+\\frac{\\sqrt{3}}{2 \\sqrt{2}}\\\\
    \\displaystyle &=&\\frac{\\sqrt{2}+\\sqrt{6}}{4}
    \\end{eqnarray}<\/p>\n\n\n\n

    \\begin{eqnarray}
    \\displaystyle \\sin \\frac{\\pi}{12}&=&\\sin (\\frac{\\pi}{3}-\\frac{\\pi}{4})\\\\
    \\displaystyle &=&\\sin \\frac{\\pi}{3} \\cos \\frac{\\pi}{4}-\\cos \\frac{\\pi}{3} \\sin \\frac{\\pi}{4}\\\\
    \\displaystyle &=&\\frac{\\sqrt{3}}{2 \\sqrt{2}}-\\frac{1}{2 \\sqrt{2}}\\\\
    \\displaystyle &=&\\frac{\\sqrt{6}+\\sqrt{2}}{4}
    \\end{eqnarray}<\/p>\n\n\n\n

    \\(\\cos\\)\u306e\u52a0\u6cd5\u5b9a\u7406<\/h3>\n\n\n\n

    \\(\\cos\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

    \u52a0\u6cd5\u5b9a\u7406<\/span><\/div>
    \n

    \\begin{eqnarray}
    \\cos(\\alpha+\\beta)=\\cos \\alpha \\cos \\beta-\\sin \\alpha \\sin \\beta\\\\
    \\cos(\\alpha-\\beta)=\\cos \\alpha \\cos \\beta+\\sin \\alpha \\sin \\beta
    \\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

    \\(\\cos\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001<\/p>\n\n\n\n

    \\begin{eqnarray}
    \\cos 105^\\circ &=& \\cos(45^\\circ + 60^\\circ)\\\\
    &=&\\cos 45^\\circ \\cos 60^\\circ-\\sin 45^\\circ \\sin 60^\\circ\\\\
    \\displaystyle &=&\\frac{1}{2 \\sqrt{2}}-\\frac{\\sqrt{3}}{2 \\sqrt{2}}\\\\
    \\displaystyle &=&\\frac{\\sqrt{2}-\\sqrt{6}}{4}
    \\end{eqnarray}<\/p>\n\n\n\n

    \\begin{eqnarray}
    \\displaystyle \\cos \\frac{\\pi}{12}&=&\\cos (\\frac{\\pi}{3}-\\frac{\\pi}{4})\\\\
    \\displaystyle &=&\\cos \\frac{\\pi}{3} \\cos \\frac{\\pi}{4}+\\sin \\frac{\\pi}{3} \\sin \\frac{\\pi}{4}\\\\
    \\displaystyle &=&\\frac{1}{2 \\sqrt{2}}+\\frac{\\sqrt{3}}{2 \\sqrt{2}}\\\\
    \\displaystyle &=&\\frac{\\sqrt{2}+\\sqrt{6}}{4}
    \\end{eqnarray}<\/p>\n\n\n\n

    \u306a\u3069\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

    \\(\\tan\\)\u306e\u52a0\u6cd5\u5b9a\u7406<\/h3>\n\n\n\n

    \\(\\tan\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

    \u52a0\u6cd5\u5b9a\u7406<\/span><\/div>
    \n


    \\begin{eqnarray}
    \\displaystyle \\tan(\\alpha+\\beta)=\\frac{\\tan \\alpha+\\tan \\beta}{1-\\tan \\alpha \\tan \\beta}\\\\
    \\displaystyle \\tan(\\alpha-\\beta)=\\frac{\\tan \\alpha -\\tan \\beta}{1+\\tan \\alpha \\tan \\beta}
    \\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

    \\(\\tan\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3082\u4f7f\u3063\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n

    \\begin{eqnarray}
    \\tan 105^\\circ &=& \\tan(45^\\circ + 60^\\circ)\\\\
    \\displaystyle &=&\\frac{\\tan 45^\\circ+\\tan 60^\\circ}{1-\\tan 45^\\circ \\tan 60^\\circ}\\\\
    \\displaystyle &=&\\frac{1+\\sqrt{3}}{1-1 \\cdot \\sqrt{3}}\\\\
    \\displaystyle &=&\\frac{1+\\sqrt{3}}{1-\\sqrt{3}}
    \\end{eqnarray}<\/p>\n\n\n\n

    \\begin{eqnarray}
    \\displaystyle \\tan \\frac{\\pi}{12}&=&\\tan (\\frac{\\pi}{3}-\\frac{\\pi}{4})\\\\
    \\displaystyle &=&\\frac{\\tan \\frac{\\pi}{3}-\\tan \\frac{\\pi}{4}}{1+\\tan \\frac{\\pi}{3} \\tan \\frac{\\pi}{4}}\\\\
    \\displaystyle &=&\\frac{\\sqrt{3}-1}{1+\\sqrt{3} \\cdot 1}\\\\
    \\displaystyle &=&\\frac{\\sqrt{3}-1}{1+\\sqrt{3}}
    \\end{eqnarray}<\/p>\n\n\n\n

    \u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3046\u305f\u3081\u306b\u3001\u89d2\u5ea6\u306e\u8868\u3057\u65b9\u3092\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

    \u6c42\u3081\u305f\u3044\u89d2\u5ea6<\/td>\u5ea6\u6570\u6cd5<\/td>\u5f27\u5ea6\u6cd5<\/td><\/tr>
    \\(\\displaystyle 15^\\circ , \\frac{\\pi}{12}\\)<\/td>\\(45^\\circ-30^\\circ\\)<\/td>\\(\\displaystyle \\frac{\\pi}{4}-\\frac{\\pi}{6}\\)<\/td><\/tr>
    \\(\\displaystyle 75^\\circ , \\frac{5}{12}\\pi\\)<\/td>\\(45^\\circ + 30^\\circ\\)<\/td>\\(\\displaystyle \\frac{\\pi}{4}+\\frac{\\pi}{6}\\)<\/td><\/tr>
    \\(\\displaystyle 105^\\circ , \\frac{7}{12}\\pi\\)<\/td>\\(60^\\circ + 45^\\circ\\)<\/td>\\(\\displaystyle \\frac{\\pi}{3}+\\frac{\\pi}{4}\\)<\/td><\/tr>
    \\(\\displaystyle 165^\\circ , \\frac{11}{12}\\pi\\)<\/td>\\(120^\\circ+45^\\circ\\)<\/td>\\(\\displaystyle \\frac{2}{3}\\pi+\\frac{\\pi}{4}\\)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    \u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9<\/h2>\n\n\n\n

    \u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u899a\u3048\u3089\u308c\u306a\u3044\uff01\uff01\u300d<\/span><\/p>\n\n\n\n

    \u3053\u3093\u306a\u65b9\u3082\u591a\u3044\u3068\u601d\u3046\u306e\u3067\u3001\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

    \u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9<\/span><\/div>
    \n

    \\[\\sin(\\alpha \u00b1 \\beta)=\\sin \\alpha \\cos \\beta \u00b1 \\cos \\alpha \\sin \\beta\\]<\/p>\n\n\n\n

      \n
    • \u54b2\u3044\u305f\u30b3\u30b9\u30e2\u30b9\u3000\u30b3\u30b9\u30e2\u30b9\u54b2\u3044\u305f<\/li>\n\n\n\n
    • \u30b5\u30c1\u30b3\u5c0f\u6797\u3000\u5c0f\u6797\u30b5\u30c1\u30b3<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n
      \n
      \"\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9sin\"<\/figure>\n<\/div>\n\n\n
      \u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9<\/span><\/div>
      \n

      \\[\\cos(\\alpha \u00b1 \\beta)=\\cos \\alpha \\cos \\beta \u2213 \\sin \\alpha \\sin \\beta\\]<\/p>\n\n\n\n

        \n
      • \u30b3\u30b9\u30e2\u30b9\u30b3\u30b9\u30e2\u30b9\u3000\u54b2\u3044\u305f\u54b2\u3044\u305f<\/li>\n\n\n\n
      • \u96ea\u3084\u30b3\u30f3\u30b3\u30f3\u3001\u6bce\u65e5(\u30de\u30a4\u30ca\u30b9)\u3000\u30b7\u30f3\u30b7\u30f3<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n
        \n
        \"\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9cos\"<\/figure>\n<\/div>\n\n\n
        \u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9<\/span><\/div>
        \n

        \\[\\displaystyle \\tan(\u03b1\u00b1\u03b2)=\\frac{\\tan\u03b1 \u00b1 \\tan\u03b2}{1-\\tan\u03b1 \\tan\u03b2}\\]<\/p>\n\n\n\n

        \u30fb\u30bf\u30f3\u30bf\u30bf\u30f3\u3000\u3044\u307e\u7acb\u3063\u305f<\/p>\n<\/div><\/div>\n\n\n

        \n
        \"\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9tan\"<\/figure>\n<\/div>\n\n
        \"\"\u9ad8\u6821\u751f<\/span><\/div>
        \n

        \u3059\u3050\u516c\u5f0f\u3092\u5fd8\u308c\u3066\u3057\u307e\u3046\u306e\u3067\u5fc3\u914d\u3067\u3059<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

        \u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e<\/h2>\n\n\n\n

        \u52a0\u6cd5\u5b9a\u7406\u3092\u8a3c\u660e\u3059\u308b\u306b\u306f\u3001\u307e\u305a\\(\\cos\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

        \u4eca\u56de\u306f\u4f59\u5f26\u5b9a\u7406\u3092\u6d3b\u7528\u3059\u308b\u8a3c\u660e\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

        \u70b9\\(P,Q\\)\u306e\u5ea7\u6a19\u3092\\(P(\\cos \\alpha ,\\sin \\alpha),Q(\\cos \\beta ,\\sin \\beta)\\)\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n

        \n
        \"\u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e\uff1a\u4f59\u5f26\u5b9a\u7406\u3092\u4f7f\u3046\"<\/figure>\n<\/div>\n\n\n

        \u307e\u305a\u306f\u4f59\u5f26\u5b9a\u7406\u3092\u7528\u3044\u3066\\(PQ^{2}\\)\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

        \u70b9\\(P,Q\\)\u306f\u5358\u4f4d\u5186\u4e0a\u306e\u70b9\u306a\u306e\u3067\u3001\\(OP=OQ=1\\)\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n\n\n\n

        \\begin{eqnarray}
        PQ^{2}&=&OP^{2}+OQ^{2}-2OP \\cdot OQ \\cos (\\beta – \\alpha)\\\\
        &=&1+1-2\\cos(\\beta – \\alpha)\\\\
        &=&2-2 \\cos(\\alpha – \\beta) \\cdots \u2460
        \\end{eqnarray}<\/p>\n\n\n\n

        \u6b21\u306b\u70b9\\(P\\)\u3068\u70b9\\(Q\\)\u306e2\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u3082\u3068\u3081\u3066\u3001<\/p>\n\n\n\n

        \\begin{eqnarray}
        PQ^{2}&=&(\\cos \\beta -\\cos \\alpha)^{2}+(\\sin \\beta -\\sin \\alpha)^{2}\\\\
        &=&2-2\\cos \\alpha \\cos \\beta – 2 \\sin \\alpha \\sin \\beta\\\\
        &=&2-2(\\cos \\alpha \\cos \\beta +  \\sin \\alpha \\sin \\beta) \\cdots \u2461
        \\end{eqnarray}<\/p>\n\n\n\n

        \u2460,\u2461\u3088\u308a\u3001<\/p>\n\n\n\n

        \\[2-2 \\cos(\\alpha – \\beta)=2-2(\\cos \\alpha \\cos \\beta + \\sin \\alpha \\sin \\beta)\\]<\/p>\n\n\n\n

        \u3086\u3048\u306b\u3001<\/p>\n\n\n\n

        \\[2 \\cos(\\alpha – \\beta)=2(\\cos \\alpha \\cos \\beta + \\sin \\alpha \\sin \\beta)\\]<\/p>\n\n\n\n

        \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

        \\[\\cos(\\alpha – \\beta)=\\cos \\alpha \\cos \\beta +  \\sin \\alpha \\sin \\beta\\]<\/span><\/p>\n\n\n\n

        \u4f59\u5f26\u5b9a\u7406\u3092\u4f7f\u308f\u306a\u3044\u8a3c\u660e\u3082\u77e5\u308a\u305f\u3044\u65b9\u306f\u3053\u3061\u3089\u306e\u8a18\u4e8b\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

        \u21d2\u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e\u3092\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\uff012\u70b9\u306e\u8ddd\u96e2\u3068\u4f59\u5f26\u5b9a\u7406\u3067\u793a\u3081\u3059<\/p>\n\n\n\n

        \u305d\u306e\u4ed6\u306e\u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e<\/h3>\n\n\n\n

        \\(\\cos (\\alpha – \\beta)\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u793a\u305b\u308c\u3070\u3001\u305d\u306e\u4ed6\u306e\u52a0\u6cd5\u5b9a\u7406\u306f\u5f0f\u5909\u5f62\u3067\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\cos (\\alpha+\\beta)&=&\\cos \\{\\alpha-(-\\beta)\\} \\\\
        &=&\\cos \\alpha \\cos (-\\beta)+\\sin \\alpha \\sin (-\\beta)\\\\
        &=&\\cos \\alpha \\cos \\beta-\\sin \\alpha \\sin \\beta\\\\
        \\end{eqnarray}<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\sin (\\alpha+\\beta)&=&\\cos \\{90-(\\alpha+\\beta)\\}\\\\
        &=&\\cos \\{(90-\\alpha)-\\beta\\} \\\\
        &=&\\cos (90-\\alpha) \\cos \\beta+\\sin (90-\\alpha) \\sin \\beta \\\\
        &=&\\sin \\alpha \\cos \\beta+\\cos \\alpha \\sin \\beta
        \\end{eqnarray}<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\sin (\\alpha-\\beta)&=&\\sin \\{\\alpha+(-\\beta)\\} \\\\
        &=&\\sin \\alpha \\cos (-\\beta)+\\cos \\alpha \\sin (-\\beta) \\\\
        &=&\\sin \\alpha \\cos \\beta-\\cos \\alpha \\sin \\beta
        \\end{eqnarray}<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\displaystyle \\tan (\\alpha+\\beta)&=&\\frac{\\sin (\\alpha+\\beta)}{\\cos (\\alpha+\\beta)} \\\\
        \\displaystyle &=&\\frac{\\sin \\alpha \\cos \\beta+\\cos \\alpha \\sin \\beta}{\\cos \\alpha \\cos \\beta-\\sin \\alpha \\sin \\beta }
        \\end{eqnarray}<\/p>\n\n\n\n

        \u5206\u5b50, \u5206\u6bcd\u3092 \\(\\cos \\alpha \\cos \\beta\\)\u3067\u5272\u3063\u3066\u3001<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\displaystyle \u3000&=&\\frac{\\tan \\alpha+\\tan \\beta}{1-\\tan \\alpha \\tan \\beta}
        \\end{eqnarray}
        \\begin{eqnarray}
        \\displaystyle \\tan (\\alpha-\\beta)&=&\\frac{\\sin (\\alpha-\\beta)}{\\cos (\\alpha-\\beta)} \\\\
        \\displaystyle &=&\\frac{\\sin \\alpha \\cos \\beta-\\cos \\alpha \\sin \\beta}{\\cos \\alpha \\cos \\beta+\\sin \\alpha \\sin \\beta}
        \\end{eqnarray}<\/p>\n\n\n\n

        \u5206\u5b50, \u5206\u6bcd\u3092\\(\\cos \\alpha \\cos \\beta \\)\u3067\u5272\u3063\u3066\u3001<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\displaystyle &=&\\frac{\\tan \\alpha-\\tan \\beta}{1+\\tan \\alpha \\tan \\beta}
        \\end{eqnarray}<\/p>\n\n\n\n

        \u3053\u308c\u3067\u3059\u3079\u3066\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

        \u307e\u305a\u306f\\(\\cos\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u793a\u3059\u3053\u3068\u3092\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n

        2\u500d\u89d2\u306e\u516c\u5f0f<\/h2>\n\n\n\n

        \u52a0\u6cd5\u5b9a\u7406\u3092\u6d3b\u7528\u3057\u305f\u516c\u5f0f\u306b“2\u500d\u89d2\u306e\u516c\u5f0f”<\/span>\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

        2\u500d\u89d2\u306e\u516c\u5f0f<\/span><\/div>
        \n

        \\begin{eqnarray}
        \\sin 2 \\alpha&=&2 \\sin \\alpha \\cos \\alpha\\\\
        \\cos 2 \\alpha&=&\\cos^{2} \\alpha – \\sin^{2} \\alpha\\\\
        &=&1-2 \\sin^{2} \\alpha\\\\
        &=&2 \\cos^{2}-1\\\\
        \\displaystyle \\tan 2\\alpha&=&\\frac{2 \\tan \\alpha}{1-\\tan^{2}\\alpha}
        \\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

        2\u500d\u89d2\u306e\u516c\u5f0f\u306f\u52a0\u6cd5\u5b9a\u7406\u3092\u6d3b\u7528\u3057\u3066\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\sin 2 \\alpha&=&\\sin (\\alpha + \\alpha)\\\\
        &=&\\sin \\alpha \\cos \\alpha + \\cos \\alpha \\sin \\alpha\\\\
        &=&2\\sin \\alpha \\cos \\alpha
        \\end{eqnarray}<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\cos 2 \\alpha&=&\\cos (\\alpha + \\alpha)\\\\
        &=&\\cos \\alpha \\cos \\alpha – \\sin \\alpha \\sin \\alpha\\\\
        &=&\\cos^{2} \\alpha – \\sin^{2} \\alpha\\\\
        &=&(1-\\sin^{2} \\alpha) – \\sin^{2} \\alpha\\\\
        &=&1-2 \\sin^{2} \\alpha
        \\end{eqnarray}<\/p>\n\n\n\n

        2\u500d\u89d2\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u306f\u5225\u306e\u8a18\u4e8b\u3067\u8a73\u3057\u304f\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

        \u534a\u89d2\u306e\u516c\u5f0f<\/h2>\n\n\n\n

        “\u534a\u89d2\u306e\u516c\u5f0f”<\/span>\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u9006\u306b\u6d3b\u7528\u3057\u305f\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

        \u534a\u89d2\u306e\u516c\u5f0f<\/span><\/div>
        \n

        \\begin{eqnarray}
        \\sin ^{2} \\frac{\\alpha}{2}&=&\\frac{1-\\cos \\alpha}{2}\\\\
        \\cos ^{2} \\frac{\\alpha}{2}&=&\\frac{1+\\cos \\alpha}{2}\\\\
        \\tan ^{2} \\frac{\\alpha}{2}&=&\\frac{1-\\cos \\alpha}{1+\\cos \\alpha}
        \\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

        \\(\\cos \\alpha\\)\u304c\u5206\u304b\u3063\u3066\u3044\u308c\u3070\u3001\\(\\displaystyle \\frac{\\alpha}{2}\\)\u306b\u95a2\u3059\u308b\u4e09\u89d2\u6bd4\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/p>\n\n\n\n

        \u534a\u89d2\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u306f\u3053\u3061\u3089<\/p>\n\n\n\n

        \u52a0\u6cd5\u5b9a\u7406\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n

        \u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3063\u305f\u7df4\u7fd2\u554f\u984c\u306b\u30c1\u30e3\u30ec\u30f3\u30b8\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

        \u7df4\u7fd2\u554f\u984c1<\/span><\/div>
        \n

        \u6b21\u306e\u5024\u306e\u6c42\u3081\u3088\u3046\u3002<\/p>\n\n\n\n

        (1)\\(\\cos 75^\\circ\\)<\/p>\n\n\n\n

        (2)\\(\\displaystyle \\sin \\frac{7}{12}\\pi\\)<\/p>\n<\/div><\/div>\n\n\n\n

        \\begin{eqnarray}
        \\cos 75^\\circ&=&\\cos(30^\\circ +45^\\circ)\\\\
        &=&\\cos 30^\\circ \\cos 45^\\circ- \\sin 30^\\circ \\sin 45^\\circ\\\\
        \\displaystyle &=&\\frac{\\sqrt{3}}{2} \\times \\frac{1}{\\sqrt{2}} – \\frac{1}{2} \\times \\frac{1}{\\sqrt{2}}\\\\
        \\displaystyle &=&\\frac{\\sqrt{6}- \\sqrt{2}}{4}
        \\end{eqnarray}<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\displaystyle \\sin \\frac{7}{12}\\pi&=&\\sin(\\frac{\\pi}{3} + \\frac{\\pi}{4})\\\\
        &=&\\sin \\frac{\\pi}{3} \\cos \\frac{\\pi}{4} + \\cos \\frac{\\pi}{3} \\sin \\frac{\\pi}{4}\\\\
        \\displaystyle &=&\\frac{\\sqrt{3}}{2} \\times \\frac{1}{\\sqrt{2}} + \\frac{1}{2} \\times \\frac{1}{\\sqrt{2}}\\\\
        \\displaystyle &=&\\frac{\\sqrt{6} + \\sqrt{2}}{4}
        \\end{eqnarray}<\/p>\n\n\n\n

        \u7df4\u7fd2\u554f\u984c2<\/span><\/div>
        \n

        \\(\\displaystyle \\frac{\\pi}{2}\\ <\\alpha <\\pi ,0 <\\beta <\\frac{\\pi}{2}\\)\u306b\u304a\u3044\u3066\u3001<\/p>\n\n\n\n

        \\(\\sin \\alpha=\\frac{3}{5},\\cos \\beta =\\frac{1}{2}\\)\u306e\u3068\u304d\u3001<\/p>\n\n\n\n

        \\(\\sin(\\alpha + \\beta)\\)\u306e\u5024\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n<\/div><\/div>\n\n\n\n

        \\[\\sin(\\alpha + \\beta)=\\sin \\alpha \\cos \\beta+ \\cos \\alpha \\sin \\beta \\cdots \u2460\\]<\/p>\n\n\n\n

        \u306a\u306e\u3067\u3001<\/p>\n\n\n\n

        \\(\\cos \\alpha,\\sin \\beta\\)\u3092\u6c42\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\cos^{2} \\alpha&=&1-\\sin^{2} \\alpha\\\\
        \\displaystyle &=&1-\\left(\\frac{3}{5}\\right)^{2}\\\\
        &=&\\frac{16}{25}
        \\end{eqnarray}<\/p>\n\n\n\n

        \\(\\displaystyle \\frac{\\pi}{2} < \\alpha < \\pi\\)\u3088\u308a\u3001\\(\\cos \\alpha<0\\)<\/p>\n\n\n\n

        \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

        \\[\\displaystyle \\cos \\alpha =\\frac{4}{5} \\cdots \u2461\\]<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\sin^{2} \\beta&=&1-\\cos^{2} \\beta\\\\
        \\displaystyle &=&1-\\left(\\frac{1}{2}\\right)^{2}\\\\
        &=&\\frac{3}{4}
        \\end{eqnarray}<\/p>\n\n\n\n

        \\(\\displaystyle 0 < \\beta < \\frac{\\pi}{2}\\)\u3088\u308a\u3001\\(\\sin \\beta<0\\)<\/p>\n\n\n\n

        \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

        \\[\\displaystyle \\sin \\beta=\\frac{\\sqrt{3}}{2} \\cdots \u2462\\]<\/p>\n\n\n\n

        \u2460,\u2461,\u2462\u3088\u308a\u3001<\/p>\n\n\n\n

        \\begin{eqnarray}
        \\sin(\\alpha + \\beta)&=&\\sin \\alpha \\cos \\beta+ \\cos \\alpha \\sin \\beta\\\\
        \\displaystyle &=&\\frac{3}{5} \\times \\frac{1}{2}+\\frac{4}{5} \\times \\frac{\\sqrt{3}}{2}\\\\
        \\displaystyle &=&\\frac{3+4\\sqrt{3}}{10}
        \\end{eqnarray}<\/p>\n\n\n\n

        \u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

        \\[\\displaystyle\\sin(\\alpha + \\beta)=\\frac{3+4\\sqrt{3}}{10}\\]<\/span><\/p>\n\n\n

        \"\"\u9ad8\u6821\u751f<\/span><\/div>
        \n

        \u306a\u3093\u3068\u304b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\uff01\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

        \u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n

        \u4eca\u56de\u306f\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n

        \u52a0\u6cd5\u5b9a\u7406<\/span><\/div>
        \n

        \\begin{eqnarray}
        \\sin(\\alpha+\\beta)&=&\\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta\\\\
        \\sin(\\alpha-\\beta)&=&\\sin \\alpha \\cos \\beta-\\cos \\alpha \\sin \\beta\\\\
        \\cos(\\alpha+\\beta)&=&\\cos \\alpha \\cos \\beta-\\sin \\alpha \\sin \\beta\\\\
        \\cos(\\alpha-\\beta)&=&\\cos \\alpha \\cos \\beta+\\sin \\alpha \\sin \\beta\\\\
        \\displaystyle \\tan(\\alpha+\\beta)&=&\\frac{\\tan \\alpha+\\tan \\beta}{1-\\tan \\alpha \\tan \\beta}\\\\
        \\displaystyle \\tan(\\alpha-\\beta)&=&\\frac{\\tan \\alpha -\\tan \\beta}{1+\\tan \\alpha \\tan \\beta}
        \\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

        \\(\\sin 105^\\circ\\)\u3084\\(\\displaystyle \\cos \\frac{\\pi}{12}\\)\u304c\u7a81\u7136\u51fa\u3066\u304f\u308b\u3068\u30d3\u30c3\u30af\u30ea\u3057\u307e\u3059\u304c\u3001\u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3048\u3070\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n

        \u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306f\u8907\u96d1\u306a\u516c\u5f0f\u3067\u3059\u304c\u3001\u6642\u9593\u3092\u304b\u3051\u3066\u3067\u3082\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n\n\n\n

        \u52a0\u6cd5\u5b9a\u7406\u306e\u307b\u304b\u306b\u3082\u4e09\u89d2\u95a2\u6570\u306b\u306f\u91cd\u8981\u306a\u516c\u5f0f\u304c\u305f\u304f\u3055\u3093\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

        \u4e09\u89d2\u6bd4\u3084\u4e09\u89d2\u95a2\u6570\u306b\u95a2\u3059\u308b\u8a18\u4e8b\u3092\u30d4\u30c3\u30af\u30a2\u30c3\u30d7\u3057\u305f\u306e\u3067\u3001\u305c\u3072\u53c2\u8003\u306b\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

        \u307f\u3093\u306a\u306e\u52aa\u529b\u304c\u5831\u308f\u308c\u307e\u3059\u3088\u3046\u306b\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u300c\u52a0\u6cd5\u5b9a\u7406\u3063\u3066\u306a\u3093\u3060\u3063\u3051\uff1f\u300d\u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u77e5\u308a\u305f\u3044\u300d\u4eca\u56de\u306f\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u4e09\u89d2\u95a2\u6570\u306e\u306a\u304b\u3067\u3082\u52a0\u6cd5\u5b9a\u7406\u306f\u91cd\u8981\u306a\u516c\u5f0f\u306e1\u3064\u3067\u3059\u3002 \u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001\\(\\sin 105^\\circ\\)\u3084\\( […]<\/p>\n","protected":false},"author":1,"featured_media":6729,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[35,224],"tags":[36,14,11],"class_list":["post-6673","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sincos","category-math-2","tag-36","tag-b","tag-11"],"yoast_head":"\n\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac\" \/>\n<meta property=\"og:description\" content=\"\u300c\u52a0\u6cd5\u5b9a\u7406\u3063\u3066\u306a\u3093\u3060\u3063\u3051\uff1f\u300d\u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u77e5\u308a\u305f\u3044\u300d\u4eca\u56de\u306f\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u4e09\u89d2\u95a2\u6570\u306e\u306a\u304b\u3067\u3082\u52a0\u6cd5\u5b9a\u7406\u306f\u91cd\u8981\u306a\u516c\u5f0f\u306e1\u3064\u3067\u3059\u3002 \u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001(sin 105^circ)\u3084( […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/\" \/>\n<meta property=\"og:site_name\" content=\"\u30de\u30b9\u30c8\u30e9\u9ad8\u6821\u6570\u5b66\u307e\u3068\u3081\u30b5\u30a4\u30c8\" \/>\n<meta property=\"article:published_time\" content=\"2025-12-24T08:19:15+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-02-11T07:29:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"630\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"\u3086\u3046\u3084\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@https:\/\/twitter.com\/mathtora\" \/>\n<meta name=\"twitter:label1\" content=\"\u57f7\u7b46\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u3086\u3046\u3084\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u63a8\u5b9a\u8aad\u307f\u53d6\u308a\u6642\u9593\" \/>\n\t<meta name=\"twitter:data2\" content=\"25\u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/\"},\"author\":{\"name\":\"\u3086\u3046\u3084\",\"@id\":\"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395\"},\"headline\":\"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac\",\"datePublished\":\"2025-12-24T08:19:15+00:00\",\"dateModified\":\"2026-02-11T07:29:18+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/\"},\"wordCount\":1446,\"commentCount\":0,\"image\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png\",\"keywords\":[\"\u4e09\u89d2\u95a2\u6570\",\"\u6570\u5b66\u2161B\",\"\u9ad8\u6821\u6570\u5b66\"],\"articleSection\":[\"\u4e09\u89d2\u95a2\u6570\",\"\u6570\u5b662\"],\"inLanguage\":\"ja\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/\",\"url\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/\",\"name\":\"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac\",\"isPartOf\":{\"@id\":\"https:\/\/math-travel.jp\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png\",\"datePublished\":\"2025-12-24T08:19:15+00:00\",\"dateModified\":\"2026-02-11T07:29:18+00:00\",\"author\":{\"@id\":\"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395\"},\"breadcrumb\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#breadcrumb\"},\"inLanguage\":\"ja\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"ja\",\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#primaryimage\",\"url\":\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png\",\"contentUrl\":\"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png\",\"width\":1200,\"height\":630,\"caption\":\"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff01\u52a0\u6cd5\u5b9a\u7406\u306e\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u5fb9\u5e95\u89e3\u8aac\uff01\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u30de\u30b9\u30c8\u30e9TOP\u30da\u30fc\u30b8\",\"item\":\"https:\/\/math-travel.jp\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u6570\u5b662\",\"item\":\"https:\/\/math-travel.jp\/math-2\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/math-travel.jp\/#website\",\"url\":\"https:\/\/math-travel.jp\/\",\"name\":\"\u30de\u30b9\u30c8\u30e9\u9ad8\u6821\u6570\u5b66\u307e\u3068\u3081\u30b5\u30a4\u30c8\",\"description\":\"\u9ad8\u6821\u6570\u5b66\u307e\u3068\u3081\u30b5\u30a4\u30c8\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/math-travel.jp\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"ja\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395\",\"name\":\"\u3086\u3046\u3084\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ja\",\"@id\":\"https:\/\/math-travel.jp\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/4d305e300a68567ef8b0fcf2b1b0f737d3d5554876534b905de84ae49b754859?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/4d305e300a68567ef8b0fcf2b1b0f737d3d5554876534b905de84ae49b754859?s=96&d=mm&r=g\",\"caption\":\"\u3086\u3046\u3084\"},\"description\":\"\u6570\u5b66\u6559\u80b2\u5c02\u9580\u5bb6\u30fb\u30aa\u30f3\u30e9\u30a4\u30f3\u5bb6\u5ead\u6559\u5e2b\u300c\u30b9\u30bf\u30c7\u30a3\u30c8\u30ec\u30fc\u30ca\u30fc\u300d\u4ee3\u8868 \u611b\u77e5\u6559\u80b2\u5927\u5b66\u6559\u80b2\u5b66\u90e8\u6570\u5b66\u9078\u4fee\u3092\u5352\u696d\u3002\u5c0f\u5b66\u6821\u30fb\u4e2d\u5b66\u6821\u30fb\u9ad8\u7b49\u5b66\u6821\u306e\u6559\u54e1\u514d\u8a31\u3092\u4fdd\u6301\u3057\u3001\u5b9f\u7528\u6570\u5b66\u6280\u80fd\u691c\u5b9a\u6e961\u7d1a\u3092\u6240\u6301\u3002 \u500b\u5225\u6307\u5c0e\u6b7410\u5e74\u3001\u3053\u308c\u307e\u3067\u306b\u6570\u767e\u540d\u4ee5\u4e0a\u306e\u53d7\u9a13\u751f\u3092\u76f4\u63a5\u6307\u5c0e\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u6559\u79d1\u66f8\u306e\u300c\u884c\u9593\u300d\u306b\u3042\u308b\u8ad6\u7406\u3092\u8a00\u8a9e\u5316\u3057\u3001\u6697\u8a18\u306b\u983c\u3089\u306a\u3044\u300c\u672c\u8cea\u7684\u306a\u6570\u5b66\u306e\u697d\u3057\u3055\u300d\u3092\u4f1d\u3048\u308b\u3053\u3068\u3092\u4fe1\u6761\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u73fe\u5728\u306f\u3001\u5168\u56fd\u306e\u751f\u5f92\u3092\u5bfe\u8c61\u3068\u3057\u305f\u30aa\u30f3\u30e9\u30a4\u30f3\u5bb6\u5ead\u6559\u5e2b\u300c\u30b9\u30bf\u30c7\u30a3\u30c8\u30ec\u30fc\u30ca\u30fc\u300d\u3092\u904b\u55b6\u3057\u3001\u504f\u5dee\u502440\u53f0\u304b\u3089\u306e\u9006\u8ee2\u5408\u683c\u3084\u3001\u6570\u5b66\u30a2\u30ec\u30eb\u30ae\u30fc\u306e\u514b\u670d\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u307e\u3059\u3002\",\"sameAs\":[\"https:\/\/www.instagram.com\/mathtora\/\",\"https:\/\/x.com\/https:\/\/twitter.com\/mathtora\",\"https:\/\/www.youtube.com\/channel\/UCH36B2btgm4soZodctY1SJQ\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/","og_locale":"ja_JP","og_type":"article","og_title":"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac","og_description":"\u300c\u52a0\u6cd5\u5b9a\u7406\u3063\u3066\u306a\u3093\u3060\u3063\u3051\uff1f\u300d\u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u77e5\u308a\u305f\u3044\u300d\u4eca\u56de\u306f\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u4e09\u89d2\u95a2\u6570\u306e\u306a\u304b\u3067\u3082\u52a0\u6cd5\u5b9a\u7406\u306f\u91cd\u8981\u306a\u516c\u5f0f\u306e1\u3064\u3067\u3059\u3002 \u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001(sin 105^circ)\u3084( […]","og_url":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/","og_site_name":"\u30de\u30b9\u30c8\u30e9\u9ad8\u6821\u6570\u5b66\u307e\u3068\u3081\u30b5\u30a4\u30c8","article_published_time":"2025-12-24T08:19:15+00:00","article_modified_time":"2026-02-11T07:29:18+00:00","og_image":[{"width":1200,"height":630,"url":"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png","type":"image\/png"}],"author":"\u3086\u3046\u3084","twitter_card":"summary_large_image","twitter_creator":"@https:\/\/twitter.com\/mathtora","twitter_misc":{"\u57f7\u7b46\u8005":"\u3086\u3046\u3084","\u63a8\u5b9a\u8aad\u307f\u53d6\u308a\u6642\u9593":"25\u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#article","isPartOf":{"@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/"},"author":{"name":"\u3086\u3046\u3084","@id":"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395"},"headline":"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac","datePublished":"2025-12-24T08:19:15+00:00","dateModified":"2026-02-11T07:29:18+00:00","mainEntityOfPage":{"@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/"},"wordCount":1446,"commentCount":0,"image":{"@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#primaryimage"},"thumbnailUrl":"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png","keywords":["\u4e09\u89d2\u95a2\u6570","\u6570\u5b66\u2161B","\u9ad8\u6821\u6570\u5b66"],"articleSection":["\u4e09\u89d2\u95a2\u6570","\u6570\u5b662"],"inLanguage":"ja","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/math-travel.jp\/math-2\/addition-theorem\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/","url":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/","name":"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac","isPartOf":{"@id":"https:\/\/math-travel.jp\/#website"},"primaryImageOfPage":{"@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#primaryimage"},"image":{"@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#primaryimage"},"thumbnailUrl":"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png","datePublished":"2025-12-24T08:19:15+00:00","dateModified":"2026-02-11T07:29:18+00:00","author":{"@id":"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395"},"breadcrumb":{"@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#breadcrumb"},"inLanguage":"ja","potentialAction":[{"@type":"ReadAction","target":["https:\/\/math-travel.jp\/math-2\/addition-theorem\/"]}]},{"@type":"ImageObject","inLanguage":"ja","@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#primaryimage","url":"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png","contentUrl":"https:\/\/math-travel.jp\/wp-content\/uploads\/2021\/08\/\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f.png","width":1200,"height":630,"caption":"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff01\u52a0\u6cd5\u5b9a\u7406\u306e\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u5fb9\u5e95\u89e3\u8aac\uff01"},{"@type":"BreadcrumbList","@id":"https:\/\/math-travel.jp\/math-2\/addition-theorem\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u30de\u30b9\u30c8\u30e9TOP\u30da\u30fc\u30b8","item":"https:\/\/math-travel.jp\/"},{"@type":"ListItem","position":2,"name":"\u6570\u5b662","item":"https:\/\/math-travel.jp\/math-2\/"},{"@type":"ListItem","position":3,"name":"\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u307e\u3068\u3081\uff1a\u8a9e\u5442\u5408\u308f\u305b\u3067\u4e00\u751f\u5fd8\u308c\u306a\u3044\u899a\u3048\u65b9\u3068\u91cd\u8981\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac"}]},{"@type":"WebSite","@id":"https:\/\/math-travel.jp\/#website","url":"https:\/\/math-travel.jp\/","name":"\u30de\u30b9\u30c8\u30e9\u9ad8\u6821\u6570\u5b66\u307e\u3068\u3081\u30b5\u30a4\u30c8","description":"\u9ad8\u6821\u6570\u5b66\u307e\u3068\u3081\u30b5\u30a4\u30c8","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/math-travel.jp\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"ja"},{"@type":"Person","@id":"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395","name":"\u3086\u3046\u3084","image":{"@type":"ImageObject","inLanguage":"ja","@id":"https:\/\/math-travel.jp\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/4d305e300a68567ef8b0fcf2b1b0f737d3d5554876534b905de84ae49b754859?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/4d305e300a68567ef8b0fcf2b1b0f737d3d5554876534b905de84ae49b754859?s=96&d=mm&r=g","caption":"\u3086\u3046\u3084"},"description":"\u6570\u5b66\u6559\u80b2\u5c02\u9580\u5bb6\u30fb\u30aa\u30f3\u30e9\u30a4\u30f3\u5bb6\u5ead\u6559\u5e2b\u300c\u30b9\u30bf\u30c7\u30a3\u30c8\u30ec\u30fc\u30ca\u30fc\u300d\u4ee3\u8868 \u611b\u77e5\u6559\u80b2\u5927\u5b66\u6559\u80b2\u5b66\u90e8\u6570\u5b66\u9078\u4fee\u3092\u5352\u696d\u3002\u5c0f\u5b66\u6821\u30fb\u4e2d\u5b66\u6821\u30fb\u9ad8\u7b49\u5b66\u6821\u306e\u6559\u54e1\u514d\u8a31\u3092\u4fdd\u6301\u3057\u3001\u5b9f\u7528\u6570\u5b66\u6280\u80fd\u691c\u5b9a\u6e961\u7d1a\u3092\u6240\u6301\u3002 \u500b\u5225\u6307\u5c0e\u6b7410\u5e74\u3001\u3053\u308c\u307e\u3067\u306b\u6570\u767e\u540d\u4ee5\u4e0a\u306e\u53d7\u9a13\u751f\u3092\u76f4\u63a5\u6307\u5c0e\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u6559\u79d1\u66f8\u306e\u300c\u884c\u9593\u300d\u306b\u3042\u308b\u8ad6\u7406\u3092\u8a00\u8a9e\u5316\u3057\u3001\u6697\u8a18\u306b\u983c\u3089\u306a\u3044\u300c\u672c\u8cea\u7684\u306a\u6570\u5b66\u306e\u697d\u3057\u3055\u300d\u3092\u4f1d\u3048\u308b\u3053\u3068\u3092\u4fe1\u6761\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u73fe\u5728\u306f\u3001\u5168\u56fd\u306e\u751f\u5f92\u3092\u5bfe\u8c61\u3068\u3057\u305f\u30aa\u30f3\u30e9\u30a4\u30f3\u5bb6\u5ead\u6559\u5e2b\u300c\u30b9\u30bf\u30c7\u30a3\u30c8\u30ec\u30fc\u30ca\u30fc\u300d\u3092\u904b\u55b6\u3057\u3001\u504f\u5dee\u502440\u53f0\u304b\u3089\u306e\u9006\u8ee2\u5408\u683c\u3084\u3001\u6570\u5b66\u30a2\u30ec\u30eb\u30ae\u30fc\u306e\u514b\u670d\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u307e\u3059\u3002","sameAs":["https:\/\/www.instagram.com\/mathtora\/","https:\/\/x.com\/https:\/\/twitter.com\/mathtora","https:\/\/www.youtube.com\/channel\/UCH36B2btgm4soZodctY1SJQ"]}]}},"_links":{"self":[{"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/posts\/6673","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/comments?post=6673"}],"version-history":[{"count":49,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/posts\/6673\/revisions"}],"predecessor-version":[{"id":21482,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/posts\/6673\/revisions\/21482"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/media\/6729"}],"wp:attachment":[{"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/media?parent=6673"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/categories?post=6673"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/tags?post=6673"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}