{"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> \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 \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 \u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001 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 \\begin{eqnarray} \\(\\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 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\u306f\u52a0\u6cd5\u5b9a\u7406\u3092\u5fdc\u7528\u3057\u305f\u516c\u5f0f\u3067\u3059\u3002<\/span><\/p>\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\\)\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 \\(\\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} \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\\)\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\\)\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} \u540c\u69d8\u306b\u3001<\/p>\n\n\n\n \\begin{eqnarray} \u3057\u305f\u304c\u3063\u3066\u3001\\(\\cos\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/p>\n\n\n\n \\begin{eqnarray} \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\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\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 \\(\\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} \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 \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 \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 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 \\begin{eqnarray} 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 \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\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 \\(\\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} \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 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 \\(\\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} \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 \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 \\begin{eqnarray} \\(\\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 \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":"\n
\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>
<\/figure>\n<\/div>\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>
\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n2\u500d\u89d2\u306e\u516c\u5f0f<\/h2>\n\n\n\n
\\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
<\/figure>\n<\/div>\n\n
\u9ad8\u6821\u751f<\/span><\/div>2\u500d\u89d2\u306e\u516c\u5f0f\u306e\u6c42\u3081\u65b9<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\\(\\sin\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
\\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\\(\\cos\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n
\\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 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
\\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
\\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\\(\\tan\\)\u306e2\u500d\u89d2\u306e\u516c\u5f0f<\/h3>\n\n\n\n
2\u500d\u89d2\u306e\u516c\u5f0f\u3000\u4f7f\u3044\u65b9<\/h2>\n\n\n\n
\\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
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>\u300a\u5fdc\u7528\u300b\u534a\u89d2\u306e\u516c\u5f0f<\/h2>\n\n\n\n
\\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
<\/figure>\n<\/div>\n\n\n2\u500d\u89d2\u306e\u516c\u5f0f\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n
\\displaystyle \\cos 2 \\theta&=&1-2 \\left(\\frac{4}{5} \\right)^{2}\\\\
\\displaystyle &=&-\\frac{7}{25}
\\end{eqnarray}<\/p>\n\n\n\n
\\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
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\n2\u500d\u89d2\u306e\u516c\u5f0f\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n
\\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
<\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"