{"id":2138,"date":"2025-12-24T17:19:15","date_gmt":"2025-12-24T08:19:15","guid":{"rendered":"https:\/\/math-travel.com\/?p=2138"},"modified":"2026-01-28T01:37:09","modified_gmt":"2026-01-27T16:37:09","slug":"kahouteiri","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/kahouteiri\/","title":{"rendered":"\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u30925\u3064\u7d39\u4ecb\uff01\u3053\u308c\u3067\u30c6\u30b9\u30c8\u3067\u3082\u56f0\u3089\u306a\u3044\uff01"},"content":{"rendered":"\n
\u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u899a\u3048\u3089\u308c\u306a\u3044\u300d<\/span> \u6bce\u56de\u5fd8\u308c\u3066\u3057\u307e\u3046\u306e\u3067\u899a\u3048\u65b9\u304c\u77e5\u308a\u305f\u3044\u3067\u3059\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u4e09\u89d2\u5f62\u306e\u52a0\u6cd5\u5b9a\u7406\u3057\u3063\u304b\u308a\u3068\u899a\u3048\u3089\u308c\u3066\u3044\u307e\u3059\u304b\uff1f<\/p>\n\n\n\n \\begin{eqnarray} \u300c\u54b2\u3044\u305f\u30b3\u30b9\u30e2\u30b9\u3000\u30b3\u30b9\u30e2\u30b9\u54b2\u3044\u305f\u300d<\/span>\u306a\u3069\u8a9e\u5442\u5408\u308f\u305b\u3066\u899a\u3048\u3066\u3044\u308b\u65b9\u3082\u591a\u3044\u306e\u3067\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n\n\n\n \u672c\u8a18\u4e8b\u3067\u306f\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u3092\u8a9e\u5442\u5408\u308f\u305b\u3067\uff15\u3064\u7d39\u4ecb<\/span>\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u81ea\u5206\u304c1\u756a\u6c17\u306b\u5165\u3063\u305f\u8a9e\u5442\u5408\u308f\u305b\u3067\u899a\u3048\u3066\u3057\u307e\u3044\u307e\u3057\u3087\u3046\uff01<\/p>\n\n\n \u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001 \u52a0\u6cd5\u5b9a\u7406\u306f\u4e09\u89d2\u95a2\u6570\u306e\u91cd\u8981\u516c\u5f0f\u306e\uff11\u3064<\/span>\u3067\u3059\u3002<\/p>\n\n\n\n \u4ee5\u4e0b\u306b\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u4e00\u89a7\u3092\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u52a0\u6cd5\u5b9a\u7406\u306f\\(\\sin\\)\u306a\u3069\u304c\u305f\u304f\u3055\u3093\u4e26\u3093\u3067\u3044\u3066\u3001\u899a\u3048\u3065\u3089\u3044\u516c\u5f0f\u3067\u3059\u306d\u3002<\/p>\n\n\n\n \u516c\u5f0f\u3092\u4e38\u6697\u8a18\u3059\u308b\u306e\u306f\u5927\u5909\u306a\u306e\u3067\u3001\u8a9e\u5442\u5408\u308f\u305b\u3067\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u307e\u305a\u306f\u30b5\u30a4\u30f3\u306e\u52a0\u6cd5\u5b9a\u7406\u304b\u3089\u899a\u3048\u65b9\u3067\u3059\u3002<\/p>\n\n\n\n \u7b26\u53f7\u304c\u9006\u306b\u306a\u308b\u3053\u3068\u3082\u306a\u3044\u306e\u3067\u3001\u6bd4\u8f03\u7684\u899a\u3048\u3084\u3059\u3044\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n \\[\\sin(\\alpha \u00b1 \\beta)=\\sin \\alpha \\cos \\beta \u00b1 \\cos \\alpha \\sin \\beta\\]<\/p>\n\n\n\n \u6b21\u306b\u30b3\u30b5\u30a4\u30f3\u306e\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u3067\u3059\u3002<\/p>\n\n\n\n \u30b3\u30b5\u30a4\u30f3\u306e\u52a0\u6cd5\u5b9a\u7406\u306f\u5de6\u8fba\u3068\u53f3\u8fba\u3067\u7b26\u53f7\u304c\u9006\u306a\u306e\u3067\u6ce8\u610f<\/span>\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\[\\cos(\\alpha \u00b1 \\beta)=\\cos \\alpha \\cos \\beta \u2213 \\sin \\alpha \\sin \\beta\\]<\/p>\n\n\n\n \u6700\u5f8c\u306b\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u899a\u3048\u65b9\u3067\u3059\u3002<\/p>\n\n\n\n \u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u52a0\u6cd5\u5b9a\u7406\u306f\u4ed6\u306e2\u3064\u3068\u306f\u7570\u306a\u308a\u3001\u5206\u6570\u306e\u5f62\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\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 \u4eca\u56de\u306f\u5de6\u8fba\u304c\u52a0\u6cd5\u306e\u3068\u304d\u306e\u899a\u3048\u65b9\u3092\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n \u5de6\u8fba\u304c\u6e1b\u6cd5\uff08\u30de\u30a4\u30ca\u30b9\uff09\u306e\u3068\u304d\u3001\u53f3\u8fba\u306e\u7b26\u53f7\u3082\u5909\u308f\u308b\u306e\u3067\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/span><\/p>\n\n\n\n \u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u304c\u3001<\/p>\n\n\n\n \u300c\u52a0\u6cd5\u5b9a\u7406\u306f\u3069\u3046\u3057\u3066\u305d\u3093\u306a\u516c\u5f0f\u306b\u306a\u308b\u306e\uff1f\u300d<\/span><\/p>\n\n\n\n \u305d\u3046\u601d\u3046\u65b9\u3082\u3044\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n\n\n\n \u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u306f\u3001\u5358\u4f4d\u5186\u4e0a\u306e2\u70b9\u306e\u8ddd\u96e2\u3092\u7528\u3044\u3066\u8a3c\u660e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\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 \\begin{eqnarray} 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} \\begin{eqnarray} 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”<\/span>\u306f2\u500d\u89d2\u306e\u516c\u5f0f\u3092\u9006\u306b\u6d3b\u7528\u3057\u305f\u516c\u5f0f\u3067\u3059\u3002<\/p>\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 \u3053\u3053\u307e\u3067\u89e3\u8aac\u3057\u3066\u304d\u305f\u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3063\u3066\u3001\u7df4\u7fd2\u554f\u984c\u306b\u6311\u6226\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \u6b21\u306e\u5024\u3092\u6c42\u3081\u3088\u3046\u3002<\/p>\n\n\n\n (1)\\(\\sin 75^\\circ\\)<\/p>\n\n\n\n (2)\\(\\cos 15^\\circ\\)<\/p>\n\n\n\n (3)\\(\\tan 105^\\circ\\)<\/p>\n<\/div><\/div>\n\n\n \u516c\u5f0f\u306b\u4ee3\u5165\u3059\u308c\u3070\u89e3\u3051\u3061\u3083\u3046\u3088\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \\(\\sin 75^\\circ\\)\u306f\\(\\sin(30^\\circ + 45^\\circ)\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3067\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \\(\\cos 15^\\circ\\)\u306f\\(\\cos(45^\\circ – 30^\\circ)\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3067\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \\(\\tan 105^\\circ\\)\u306f\\(\\tan(60^\\circ + 45^\\circ)\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3067\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n \\begin{eqnarray} \u516c\u5f0f\u3092\u899a\u3048\u3066\u3057\u307e\u3048\u3070\u4ee3\u5165\u3059\u308b\u3060\u3051\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n \u305d\u3046\u306a\u3093\u3060\u3088\uff01\u3060\u304b\u3089\u3053\u305d\u52a0\u6cd5\u5b9a\u7406\u306f\u3059\u3050\u306b\u899a\u3048\u3066\u3057\u307e\u304a\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n \u4eca\u56de\u306f\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n \\begin{eqnarray} \u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u30925\u3064\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \\[\\sin(\\alpha \u00b1 \\beta)=\\sin \\alpha \\cos \\beta \u00b1 \\cos \\alpha \\sin \\beta\\]<\/p>\n\n\n\n \\[\\cos(\\alpha \u00b1 \\beta)=\\cos \\alpha \\cos \\beta \u2213 \\sin \\alpha \\sin \\beta\\]<\/p>\n\n\n\n \\[\\displaystyle \\tan(\u03b1\u00b1\u03b2)=\\frac{\\tan\u03b1 \u00b1 \\tan\u03b2}{1-\\tan\u03b1 \\tan\u03b2}\\]<\/p>\n\n\n\n \u52a0\u6cd5\u5b9a\u7406\u3092\u4f7f\u3046\u3053\u3068\u3067\u3001\\(45^\\circ\\)\u3084\\(60^\\circ\\)\u4ee5\u5916\u306e\u4e09\u89d2\u6bd4\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f\u304c\u899a\u3048\u3089\u308c\u306a\u3044\u300d\u300c\u52a0\u6cd5\u5b9a\u7406\u306e\u8a9e\u5442\u5408\u308f\u305b\u304c\u77e5\u308a\u305f\u3044\u300d\u4eca\u56de\u306f\u52a0\u6cd5\u5b9a\u7406\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002 \u4e09\u89d2\u5f62\u306e\u52a0\u6cd5\u5b9a\u7406\u3057\u3063\u304b\u308a\u3068\u899a\u3048\u3089\u308c\u3066\u3044\u307e\u3059\u304b\uff1f \u300c\u54b2\u3044\u305f\u30b3\u30b9\u30e2\u30b9\u3000\u30b3\u30b9\u30e2\u30b9\u54b2\u3044\u305f\u300d\u306a\u3069\u8a9e\u5442\u5408\u308f\u305b\u3066\u899a\u3048\u3066\u3044 […]<\/p>\n","protected":false},"author":1,"featured_media":6680,"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-2138","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\u52a0\u6cd5\u5b9a\u7406\u306e\u8a9e\u5442\u5408\u308f\u305b\u304c\u77e5\u308a\u305f\u3044\u300d<\/span>
\u4eca\u56de\u306f\u52a0\u6cd5\u5b9a\u7406\u306b\u95a2\u3059\u308b\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002<\/p>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\\sin(\u03b1+\u03b2)&=&\\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta\\\\
\\sin(\u03b1-\u03b2)&=&\\sin \u03b1 \\cos\u03b2-\\cos\u03b1 \\sin\u03b2\\\\
\\cos(\u03b1+\u03b2)&=&\\cos \u03b1 \\cos\u03b2-\\sin\u03b1 \\sin\u03b2\\\\
\\cos(\u03b1-\u03b2)&=&\\cos \u03b1 \\cos \u03b2+\\sin\u03b1 \\sin\u03b2\\\\
\\displaystyle \\tan(\u03b1+\u03b2)&=&\\frac{\\tan\u03b1+\\tan\u03b2}{1-\\tan\u03b1 \\tan\u03b2}\\\\
\\displaystyle \\tan(\u03b1-\u03b2)&=&\\frac{\\tan\u03b1-\\tan\u03b2}{1+\\tan\u03b1 \\tan\u03b2}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\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\n\u52a0\u6cd5\u5b9a\u7406\u306e\u516c\u5f0f<\/h2>\n\n\n\n
\\sin(\u03b1+\u03b2)&=&\\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta\\\\
\\sin(\u03b1-\u03b2)&=&\\sin \u03b1 \\cos\u03b2-\\cos\u03b1 \\sin\u03b2\\\\
\\cos(\u03b1+\u03b2)&=&\\cos \u03b1 \\cos\u03b2-\\sin\u03b1 \\sin\u03b2\\\\
\\cos(\u03b1-\u03b2)&=&\\cos \u03b1 \\cos \u03b2+\\sin\u03b1 \\sin\u03b2\\\\
\\displaystyle \\tan(\u03b1+\u03b2)&=&\\frac{\\tan\u03b1+\\tan\u03b2}{1-\\tan\u03b1 \\tan\u03b2}\\\\
\\displaystyle \\tan(\u03b1-\u03b2)&=&\\frac{\\tan\u03b1-\\tan\u03b2}{1+\\tan\u03b1 \\tan\u03b2}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9<\/h2>\n\n\n\n
\n
\n
<\/figure>\n<\/div>\n\n\n\n
<\/figure>\n<\/div>\n\n\n
<\/figure>\n<\/div>\n\n\n\u52a0\u6cd5\u5b9a\u7406\u306e\u8a3c\u660e<\/h2>\n\n\n\n
<\/figure>\n<\/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\\\\
&=&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
\\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
\\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\u534a\u89d2\u306e\u516c\u5f0f<\/h2>\n\n\n\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{\\propto}{2}&=&\\frac{1-\\cos \\alpha}{1+\\cos \\alpha}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n\u52a0\u6cd5\u5b9a\u7406\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n\n
\u30b7\u30fc\u30bf<\/span><\/div>\u7df4\u7fd2\u554f\u984c1\u306e\u89e3\u8aac<\/h3>\n\n\n\n
\\sin 75^\\circ&=&\\sin (30^\\circ + 45^\\circ)\\\\
&=&\\sin30^\\circ \\cos45^\\circ + \\cos30^\\circ \\sin45^\\circ\\\\
\\displaystyle &=&\\frac{1}{2} \\times \\frac{1}{\\sqrt2} + \\frac{\\sqrt3}{2} \\times \\frac{1}{\\sqrt2}\\\\
\\displaystyle &=&\\frac{\\sqrt2}{4} + \\frac{\\sqrt6}{4}\\\\
\\displaystyle &=&\\frac{\\sqrt2 + \\sqrt6}{4}
\\end{eqnarray}<\/p>\n\n\n\n\u7df4\u7fd2\u554f\u984c2\u306e\u89e3\u8aac<\/h3>\n\n\n\n
\\cos 15^\\circ&=&\\cos (45^\\circ-30^\\circ)\\\\
&=&\\cos45^\\circ \\cos30^\\circ+\\sin45^\\circ \\sin30^\\circ\\\\
\\displaystyle &=&\\frac{1}{\\sqrt2} \\times \\frac{\\sqrt3}{2}+ \\frac{1}{\\sqrt2} \\times \\frac{1}{2}\\\\
\\displaystyle &=&\\frac{\\sqrt6}{4}+ \\frac{\\sqrt2}{4}\\\\
\\displaystyle &=&\\frac{\\sqrt6+\\sqrt2}{4}
\\end{eqnarray}<\/p>\n\n\n\n\u7df4\u7fd2\u554f\u984c3\u306e\u89e3\u8aac<\/h3>\n\n\n\n
\\tan 105^\\circ&=&\\tan(60^\\circ + 45^\\circ)\\\\
\\displaystyle &=&\\frac{\\tan 60^circ + \\tan 45^\\circ}{1-\\tan 60^circ \\tan 45^\\circ}\\\\
\\displaystyle &=&\\frac{\\sqrt{3}+1}{1-\\sqrt{3} \\times 1}\\\\
\\displaystyle &=&\\frac{\\sqrt{3}+1}{1-\\sqrt{3}}
\\end{eqnarray}<\/p>\n\n\n
\u9ad8\u6821\u751f<\/span><\/div>
\u30b7\u30fc\u30bf<\/span><\/div>\u52a0\u6cd5\u5b9a\u7406\u306e\u899a\u3048\u65b9\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n
\\sin(\u03b1+\u03b2)&=&\\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta\\\\
\\sin(\u03b1-\u03b2)&=&\\sin \u03b1 \\cos\u03b2-\\cos\u03b1 \\sin\u03b2\\\\
\\cos(\u03b1+\u03b2)&=&\\cos \u03b1 \\cos\u03b2-\\sin\u03b1 \\sin\u03b2\\\\
\\cos(\u03b1-\u03b2)&=&\\cos \u03b1 \\cos \u03b2+\\sin\u03b1 \\sin\u03b2\\\\
\\displaystyle \\tan(\u03b1+\u03b2)&=&\\frac{\\tan\u03b1+\\tan\u03b2}{1-\\tan\u03b1 \\tan\u03b2}\\\\
\\displaystyle \\tan(\u03b1-\u03b2)&=&\\frac{\\tan\u03b1-\\tan\u03b2}{1+\\tan\u03b1 \\tan\u03b2}
\\end{eqnarray}<\/p>\n<\/div><\/div>\n\n\n\n\n
\n
\n