{"id":2176,"date":"2025-12-24T17:19:15","date_gmt":"2025-12-24T08:19:15","guid":{"rendered":"https:\/\/math-travel.com\/?p=2176"},"modified":"2026-02-11T16:38:11","modified_gmt":"2026-02-11T07:38:11","slug":"double-angle-formula","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/","title":{"rendered":"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4"},"content":{"rendered":"\n

\u300c2\u500d\u89d2\u306e\u516c\u5f0f\u3063\u3066\u3069\u3093\u306a\u516c\u5f0f\uff1f\u300d<\/span>
\u300c\u3069\u3046\u3084\u3063\u3066\u4f7f\u3048\u3070\u3044\u3044\u306e\uff1f\u300d<\/span>
\u4eca\u56de\u306f2\u500d\u89d2\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

\u516c\u5f0f\u3092\u3059\u3050\u306b\u5fd8\u308c\u3061\u3083\u3044\u307e\u3059\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u306f\u6c7a\u3057\u3066\u96e3\u3057\u3044\u516c\u5f0f\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/span><\/p>\n\n\n

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

\u898b\u305f\u76ee\u306f\u96e3\u3057\u305d\u3046\u306b\u3082\u898b\u3048\u307e\u3059\u304c\u3001\u52a0\u6cd5\u5b9a\u7406\u3092\u5fdc\u7528\u3057\u305f\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

\u96e3\u3057\u3044\u516c\u5f0f\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u4e09\u89d2\u95a2\u6570\u306b\u304a\u3051\u308b\u91cd\u8981\u306a\u516c\u5f0f<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n

\u516c\u5f0f\u3082\u899a\u3048\u3066\u6b32\u3057\u3044\u3057\u3001\u3044\u3064\u3067\u3082\u4f7f\u3044\u3053\u306a\u305b\u308b\u3088\u3046\u306b\u7df4\u7fd2\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u89e3\u8aac<\/span>\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u8a18\u4e8b\u306e\u5f8c\u534a\u306b\u7df4\u7fd2\u554f\u984c\u3082\u3042\u308b\u306e\u3067\u30012\u500d\u89d2\u306b\u6163\u308c\u3066\u3044\u306a\u3044\u65b9\u306f\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\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

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

2\u500d\u89d2\u306e\u516c\u5f0f\u306f\\(2 \\alpha\\)\u306e\u3088\u3046\u306b\u3001\u89d2\u304c\u3042\u308b\u89d2\u306e2\u500d\u306e\u3068\u304d\u306b\u4f7f\u3046\u516c\u5f0f\u3067\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\\\\
&=&2 \\cos ^{2} \\alpha-1\\\\
&=&1-2 \\sin ^{2} \\alpha\\\\
\\displaystyle \\tan 2 \\alpha&=&\\frac{2 \\tan \\alpha}{1-\\tan ^{2} \\alpha}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\\(\\sin\\)\u3084\\(\\cos\\)\u306e\u3042\u3068\u306e\u89d2\u306e\u90e8\u5206\u304c\u30012\u500d\u306e\u5f62\u3092\u3057\u3066\u3044\u305f\u30892\u500d\u89d2\u306e\u516c\u5f0f\u3092\u4f7f\u3046\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002<\/p>\n\n\n

\n
\"2\u500d\u89d2\u306e\u516c\u5f0f\u306f2\u500d\u306e\u89d2\"<\/figure>\n<\/div>\n\n
\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

2\u500d\u306e\u3068\u304d\u306b\u4f7f\u3046\u304b\u30892\u500d\u89d2\u306e\u516c\u5f0f\u306a\u3093\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u6c42\u3081\u65b9<\/h2>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u306f\u52a0\u6cd5\u5b9a\u7406\u3092\u5fdc\u7528\u3057\u305f\u516c\u5f0f\u3067\u3059\u3002<\/span><\/p>\n\n\n

\n
\"2\u500d\u89d2\u306e\u6c42\u3081\u65b9\"<\/figure>\n<\/div>\n\n\n

\u3069\u306e\u3088\u3046\u306a\u5f0f\u5909\u5f62\u3092\u3057\u3066\u30012\u500d\u89d2\u306e\u516c\u5f0f\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u306e\u304b\u3092\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\\(\\sin\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n

\\(\\sin\\)\u3082\\(\\cos\\)\u30822\u500d\u89d2\u306e\u516c\u5f0f\u3092\u6c42\u3081\u308b\u624b\u9806\u306f\u540c\u3058\u3067\u3059\u3002<\/p>\n\n\n\n

\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u3092\u601d\u3044\u51fa\u3057\u3066\u3001\\(\\beta\\)\u3092\\(\\alpha\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\u3060\u3051\u3067\u3059\u3002<\/p>\n\n\n

\n
\"sin\u306e2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u6c42\u3081\u65b9\"<\/figure>\n<\/div>\n\n\n

\\(\\sin\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3088\u308a\u3001<\/p>\n\n\n\n

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

\u3053\u3053\u3067\\(\\beta\\)\u3092\\(\\alpha\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001<\/p>\n\n\n\n

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

\u3057\u305f\u304c\u3063\u3066\u3001\\(\\sin\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/p>\n\n\n\n

\\[\\sin 2\\alpha=2\\sin \\alpha \\cos \\alpha\\]<\/span><\/p>\n\n\n\n

\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\\(\\cos\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n

\\(\\cos\\)\u3082\\(\\sin\\)\u3068\u540c\u69d8\u306e\u624b\u9806\u3067\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

\\(\\cos\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3088\u308a\u3001<\/p>\n\n\n\n

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

\u3053\u3053\u3067\\(\\beta\\)\u3092\\(\\alpha\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001<\/p>\n\n\n\n

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

\\(\\cos\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f\u306f\u307e\u3060\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u95a2\u6570\u306e\u76f8\u4e92\u95a2\u4fc2\u3088\u308a\u3001<\/p>\n\n\n\n

\\[\\sin^{2} \\theta + \\cos^{2} \\theta=1\\]<\/p>\n\n\n\n

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

\u540c\u69d8\u306b\u3001<\/p>\n\n\n\n

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

\u3057\u305f\u304c\u3063\u3066\u3001\\(\\cos\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/p>\n\n\n\n

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

\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\\(\\tan\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n

\\(\\tan\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f\u3082\u540c\u69d8\u306b\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n

\\(\\tan\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3088\u308a\u3001<\/p>\n\n\n\n

\\[\\displaystyle \\tan(\\alpha +\\beta)=\\frac{\\tan \\alpha + \\tan \\beta}{1-\\tan \\alpha \\tan \\beta}\\]<\/p>\n\n\n\n

\\(\\beta\\)\u3092\\(\\alpha\\)\u306b\u7f6e\u304d\u63db\u3048\u3066\u3001<\/p>\n\n\n\n

\\[\\displaystyle \\tan (\\alpha +\\alpha)=\\frac{\\tan \\alpha + \\tan \\alpha}{1-\\tan \\alpha \\tan \\alpha}\\]<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001\\(\\tan\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/p>\n\n\n\n

\\[\\displaystyle \\tan 2 \\alpha=\\frac{2\\tan \\alpha}{1-\\tan^{2} \\alpha}\\]<\/span><\/p>\n\n\n\n

\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u3000\u4f7f\u3044\u65b9<\/h2>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u77e5\u3063\u3066\u3044\u3066\u3082\u3001\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u306a\u3051\u308c\u3070\u5f97\u70b9\u306b\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n

\u4f8b\u984c\u3092\u89e3\u304d\u306a\u304c\u3089\u4f7f\u3044\u65b9\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u3000\u4f8b\u984c<\/span><\/div>
\n

\\(\\displaystyle \\sin \\theta=\\frac{1}{3} \\)\u306e\u3068\u304d\u3001\\(\\sin 2 \\theta\\)\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n\n\n\n

\u305f\u3060\u3057,\\(\\displaystyle 0<\\theta<\\frac{\\pi}{2}\\)\u3068\u3059\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n

\u89e3\u7b54<\/span><\/p>\n\n\n\n

\\(\\sin 2 \\theta\\)\u3092\u6c42\u3081\u308b\u306e\u3067\u30012\u500d\u89d2\u306e\u516c\u5f0f\u3092\u4f7f\u304a\u3046\u3068\u8003\u3048\u307e\u3059\u3002<\/p>\n\n\n\n

\\[\\sin 2 \\theta=2 \\sin \\theta \\cos \\theta\\]<\/p>\n\n\n\n

\\(\\sin\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u4f7f\u3046\u306b\u306f\u3001\\(\\cos \\theta\\)\u3092\u6c42\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u306d\u3002<\/p>\n\n\n\n

\u4e09\u89d2\u5f62\u306e\u76f8\u4e92\u95a2\u4fc2\u3088\u308a<\/p>\n\n\n\n

\\[\\sin^{2} \\theta + \\cos^{2} \\theta=1\\]<\/p>\n\n\n\n

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

\\[\\displaystyle \\left(\\frac{1}{3} \\right)^{2} + \\cos^{2} \\theta =1\\]<\/p>\n\n\n\n

\\[\\displaystyle \\cos^{2} \\theta =\\frac{8}{9}\\]<\/p>\n\n\n\n

\u3053\u3053\u3067,\\(\\displaystyle 0<\\theta<\\frac{\\pi}{2}\\)\u306a\u306e\u3067\u3001<\/p>\n\n\n\n

\\[\\displaystyle \\cos \\theta =\\frac{2\\sqrt2}{3}\\]<\/p>\n\n\n\n

\\(\\displaystyle \\cos \\theta =\\frac{2\\sqrt{2}}{3}\\)\u3092\uff12\u500d\u89d2\u306e\u516c\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u3001<\/p>\n\n\n\n

\\begin{eqnarray}
\\sin 2 \\theta&=&2 \\sin \\theta \\cos \\theta\\\\
\\displaystyle &=&2 \\cdot \\frac{1}{3} \\cdot \\frac{2\\sqrt{2}}{3} \\\\
\\displaystyle &=&\\frac{4\\sqrt{2}}{9}
\\end{eqnarray}<\/p>\n\n\n\n

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

\\[\\displaystyle \\sin 2 \\theta=\\frac{4\\sqrt2}{9}\\]<\/span><\/p>\n\n\n\n

\u8a08\u7b97\u5f0f\u304b\u3089\u5206\u304b\u308b\u3088\u3046\u306b\u3001\u96e3\u3057\u3044\u8a08\u7b97\u306f\u4e00\u5207\u3042\u308a\u307e\u305b\u3093\u3002<\/span><\/p>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u899a\u3048\u3066\u3001\u516c\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u5024\u3092\u6c42\u3081\u308b\u3060\u3051\u3067\u3059\u3002<\/p>\n\n\n

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

\u96e3\u3057\u3044\u30a4\u30e1\u30fc\u30b8\u304c\u3042\u308a\u307e\u3057\u305f\u304c\u3001\u3067\u304d\u308b\u6c17\u304c\u3057\u3066\u304d\u307e\u3057\u305f\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

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

\u516c\u5f0f\u3092\u899a\u3048\u305f\u3042\u3068\u306f\u7df4\u7fd2\u3042\u308b\u306e\u307f\u3060\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u300a\u5fdc\u7528\u300b\u534a\u89d2\u306e\u516c\u5f0f<\/h2>\n\n\n\n

2\u500d\u89d2\u3092\u5fdc\u7528\u3057\u305f\u516c\u5f0f\u306b\u534a\u89d2\u306e\u516c\u5f0f<\/span>\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

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

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

2\u500d\u89d2\u306e\u516c\u5f0f\u304c\u89d2\u30922\u500d\u3057\u305f\u516c\u5f0f\u3060\u3063\u305f\u306e\u306b\u5bfe\u3057\u3066\u3001\u534a\u89d2\u306e\u516c\u5f0f\u3067\u306f\u89d2\u304c\u534a\u5206\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n

\n
\"\u534a\u89d2\u306e\u516c\u5f0f\"<\/figure>\n<\/div>\n\n\n

\u534a\u89d2\u306e\u516c\u5f0f\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u5f0f\u5909\u5f62\u3057\u305f\u3060\u3051\u306a\u306e\u3067\u3001\u3059\u3050\u306b\u4f7f\u3044\u3053\u306a\u305b\u308b\u3088\u3046\u306b\u306a\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u7528\u3044\u3066\u3001\u7df4\u7fd2\u554f\u984c\u306b\u6311\u6226\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

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

\\(\\displaystyle 0<\\theta<\\frac{\\pi}{2}, \\sin \\theta=\\frac{4}{5}\\)\u306e\u3068\u304d,<\/p>\n\n\n\n

\\[\\cos 2 \\theta,\\sin 2 \\theta\\]<\/p>\n\n\n\n

\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n<\/div><\/div>\n\n\n\n

\u89e3\u7b54<\/span><\/p>\n\n\n\n

\\[\\cos 2 \\theta=1-2 \\sin^{2} \\theta \\]<\/p>\n\n\n\n

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

\\begin{eqnarray}
\\displaystyle \\cos 2 \\theta&=&1-2 \\left(\\frac{4}{5} \\right)^{2}\\\\
\\displaystyle &=&-\\frac{7}{25}
\\end{eqnarray}<\/p>\n\n\n\n

\u4e09\u89d2\u5f62\u306e\u76f8\u4e92\u95a2\u4fc2\u3088\u308a<\/p>\n\n\n\n

\\(\\displaystyle \\sin^{2} 2 \\theta=1 – \\cos^{2} 2 \\theta\\)<\/p>\n\n\n\n

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

\\begin{eqnarray}
\\displaystyle \\sin^{2} 2 \\theta&=&1 – \\cos^{2} 2 \\theta\\\\
\\displaystyle &=&1- \\left(-\\frac{7}{25} \\right)^{2}\\\\
\\displaystyle &=&1-\\frac{49}{625}\\\\
\\displaystyle &=&\\frac{576}{625}
\\end{eqnarray}<\/p>\n\n\n\n

\\(\\displaystyle 0<\\theta<\\frac{\\pi}{2}\\)\u3088\u308a,<\/p>\n\n\n\n

\\[\\displaystyle \\sin 2\\theta=\\frac{24}{25}\\]<\/span><\/p>\n\n\n\n

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

\\(\\displaystyle 0 < \\theta < \\frac{2}{3} \\pi\\)\u306e\u3068\u304d,<\/p>\n\n\n\n

\u95a2\u6570\\(y=\\cos 2 \\theta-2 \\cos \\theta\\)\u306e\u6700\u5927\u503c\u3068\u6700\u5c0f\u503c\u3092\u6c42\u3081\u3088\u3002<\/p>\n<\/div><\/div>\n\n\n\n

\u89e3\u7b54<\/span><\/p>\n\n\n\n

\u307e\u305a\u306f\u4e0e\u3048\u3089\u308c\u305f\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\\begin{eqnarray}
y&=&\\cos 2 \\theta-2 \\cos \\theta\\\\
&=&\\left(2 \\cos ^{2} \\theta-1 \\right)-2 \\cos \\theta\\\\
&=&2\\cos ^{2} \\theta-2\\cos \\theta-1
\\end{eqnarray}<\/p>\n\n\n\n

\u53f3\u8fba\u3092\u5e73\u65b9\u5b8c\u6210\u3092\u3057\u3066\u3001<\/p>\n\n\n\n

\\[\\displaystyle 2\\cos ^{2} \\theta-2\\cos \\theta-1=2(\\cos \\theta-\\frac{1}{2})^{2}-\\frac{3}{2}\\]<\/p>\n\n\n\n

\\(\\displaystyle 0 < \\theta < \\frac{2}{3} \\pi\\)\u3088\u308a,\\(\\displaystyle -\\frac{1}{2} < \\cos \\theta < 1\\)<\/p>\n\n\n\n

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

\\(\\displaystyle \\cos \\theta=-\\frac{1}{2}\\) \u306e\u3068\u304d\u6700\u5927\u503c \\(\\displaystyle \\frac{1}{2}\\)<\/p>\n\n\n\n

\\(\\displaystyle \\cos \\theta=\\frac{1}{2}\\) \u306e\u3068\u304d\u6700\u5c0f\u503c \\(\\displaystyle -\\frac{3}{2}\\)<\/p>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n

\u4eca\u56de\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/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\\\\
&=&2 \\cos ^{2} \\alpha-1\\\\
&=&1-2 \\sin ^{2} \\alpha\\\\
\\displaystyle \\tan 2 \\alpha&=&\\frac{2 \\tan \\alpha}{1-\\tan ^{2} \\alpha}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n

\\(\\cos\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f\u3060\u3051\u30013\u30d1\u30bf\u30fc\u30f3\u306b\u5909\u5f62\u3067\u304d\u308b\u306e\u3067\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

2\u500d\u89d2\u306e\u516c\u5f0f\u306f\u52a0\u6cd5\u5b9a\u7406\u3092\u5fdc\u7528\u3057\u3066\u3001\u516c\u5f0f\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n

\n
\"2\u500d\u89d2\u306e\u6c42\u3081\u65b9\"<\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u300c2\u500d\u89d2\u306e\u516c\u5f0f\u3063\u3066\u3069\u3093\u306a\u516c\u5f0f\uff1f\u300d\u300c\u3069\u3046\u3084\u3063\u3066\u4f7f\u3048\u3070\u3044\u3044\u306e\uff1f\u300d\u4eca\u56de\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 2\u500d\u89d2\u306e\u516c\u5f0f\u306f\u6c7a\u3057\u3066\u96e3\u3057\u3044\u516c\u5f0f\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u898b\u305f\u76ee\u306f\u96e3\u3057\u305d\u3046\u306b\u3082\u898b\u3048\u307e\u3059\u304c\u3001\u52a0\u6cd5\u5b9a\u7406\u3092\u5fdc\u7528\u3057\u305f\u516c\u5f0f\u3067\u3059\u3002 \u96e3\u3057 […]<\/p>\n","protected":false},"author":1,"featured_media":6840,"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-2176","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sincos","category-math-2","tag-36","tag-b","tag-11"],"yoast_head":"\n2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4<\/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\/double-angle-formula\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4\" \/>\n<meta property=\"og:description\" content=\"\u300c2\u500d\u89d2\u306e\u516c\u5f0f\u3063\u3066\u3069\u3093\u306a\u516c\u5f0f\uff1f\u300d\u300c\u3069\u3046\u3084\u3063\u3066\u4f7f\u3048\u3070\u3044\u3044\u306e\uff1f\u300d\u4eca\u56de\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 2\u500d\u89d2\u306e\u516c\u5f0f\u306f\u6c7a\u3057\u3066\u96e3\u3057\u3044\u516c\u5f0f\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u898b\u305f\u76ee\u306f\u96e3\u3057\u305d\u3046\u306b\u3082\u898b\u3048\u307e\u3059\u304c\u3001\u52a0\u6cd5\u5b9a\u7406\u3092\u5fdc\u7528\u3057\u305f\u516c\u5f0f\u3067\u3059\u3002 \u96e3\u3057 […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/\" \/>\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=\"2026-02-11T07:38:11+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.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=\"14\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\/double-angle-formula\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/\"},\"author\":{\"name\":\"\u3086\u3046\u3084\",\"@id\":\"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395\"},\"headline\":\"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4\",\"datePublished\":\"2025-12-24T08:19:15+00:00\",\"dateModified\":\"2026-02-11T07:38:11+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/\"},\"wordCount\":579,\"commentCount\":0,\"image\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.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\/double-angle-formula\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/\",\"url\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/\",\"name\":\"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4\",\"isPartOf\":{\"@id\":\"https:\/\/math-travel.jp\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.png\",\"datePublished\":\"2025-12-24T08:19:15+00:00\",\"dateModified\":\"2026-02-11T07:38:11+00:00\",\"author\":{\"@id\":\"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395\"},\"breadcrumb\":{\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#breadcrumb\"},\"inLanguage\":\"ja\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"ja\",\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#primaryimage\",\"url\":\"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.png\",\"contentUrl\":\"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.png\",\"width\":1200,\"height\":630,\"caption\":\"2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#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\":\"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4\"}]},{\"@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":"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4","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\/double-angle-formula\/","og_locale":"ja_JP","og_type":"article","og_title":"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4","og_description":"\u300c2\u500d\u89d2\u306e\u516c\u5f0f\u3063\u3066\u3069\u3093\u306a\u516c\u5f0f\uff1f\u300d\u300c\u3069\u3046\u3084\u3063\u3066\u4f7f\u3048\u3070\u3044\u3044\u306e\uff1f\u300d\u4eca\u56de\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u306b\u95a2\u3059\u308b\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 2\u500d\u89d2\u306e\u516c\u5f0f\u306f\u6c7a\u3057\u3066\u96e3\u3057\u3044\u516c\u5f0f\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u898b\u305f\u76ee\u306f\u96e3\u3057\u305d\u3046\u306b\u3082\u898b\u3048\u307e\u3059\u304c\u3001\u52a0\u6cd5\u5b9a\u7406\u3092\u5fdc\u7528\u3057\u305f\u516c\u5f0f\u3067\u3059\u3002 \u96e3\u3057 […]","og_url":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/","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":"2026-02-11T07:38:11+00:00","og_image":[{"width":1200,"height":630,"url":"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.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":"14\u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#article","isPartOf":{"@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/"},"author":{"name":"\u3086\u3046\u3084","@id":"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395"},"headline":"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4","datePublished":"2025-12-24T08:19:15+00:00","dateModified":"2026-02-11T07:38:11+00:00","mainEntityOfPage":{"@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/"},"wordCount":579,"commentCount":0,"image":{"@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#primaryimage"},"thumbnailUrl":"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.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\/double-angle-formula\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/","url":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/","name":"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4","isPartOf":{"@id":"https:\/\/math-travel.jp\/#website"},"primaryImageOfPage":{"@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#primaryimage"},"image":{"@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#primaryimage"},"thumbnailUrl":"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.png","datePublished":"2025-12-24T08:19:15+00:00","dateModified":"2026-02-11T07:38:11+00:00","author":{"@id":"https:\/\/math-travel.jp\/#\/schema\/person\/b0d9d1e7e332261165c2f7318aa4d395"},"breadcrumb":{"@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#breadcrumb"},"inLanguage":"ja","potentialAction":[{"@type":"ReadAction","target":["https:\/\/math-travel.jp\/math-2\/double-angle-formula\/"]}]},{"@type":"ImageObject","inLanguage":"ja","@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#primaryimage","url":"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.png","contentUrl":"https:\/\/math-travel.jp\/wp-content\/uploads\/2020\/05\/2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01.png","width":1200,"height":630,"caption":"2\u500d\u89d2\u306e\u516c\u5f0f\u3068\u6c42\u3081\u65b9\uff01cos\u306e\u5909\u5f62\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3088\u3046\uff01"},{"@type":"BreadcrumbList","@id":"https:\/\/math-travel.jp\/math-2\/double-angle-formula\/#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":"2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u899a\u3048\u65b9\u3068\u5c0e\u304d\u65b9\uff1acos\u306e3\u30d1\u30bf\u30fc\u30f3\u306e\u5909\u5f62\u3092\u4f7f\u3044\u5206\u3051\u308b\u30b3\u30c4"}]},{"@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\/2176","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=2176"}],"version-history":[{"count":19,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/posts\/2176\/revisions"}],"predecessor-version":[{"id":21486,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/posts\/2176\/revisions\/21486"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/media\/6840"}],"wp:attachment":[{"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/media?parent=2176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/categories?post=2176"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-travel.jp\/wp-json\/wp\/v2\/tags?post=2176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}