{"id":836,"date":"2013-07-03T00:14:01","date_gmt":"2013-07-02T15:14:01","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=836"},"modified":"2021-09-14T08:27:26","modified_gmt":"2021-09-13T23:27:26","slug":"iks201301","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/iks201301\/","title":{"rendered":"\u533b\u79d1\u6b6f\u79d1\u59272013\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u4ee5\u4e0b\u306e\u5404\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u5b9f\u6570 \\(\\alpha , \\beta\\) \u304c \\(0 \\lt \\alpha \\lt \\dfrac{\\pi}{2}\\) , \\(0 \\lt \\beta \\lt \\dfrac{\\pi}{2}\\) , \\(\\tan \\alpha \\tan \\beta = 1\\) \u3092\u6e80\u305f\u3059\u3068\u304d, \\(\\alpha +\\beta\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u5b9f\u6570 \\(\\alpha , \\beta , \\gamma\\) \u304c \\(0 \\lt \\alpha \\lt \\dfrac{\\pi}{2}\\) , \\(0 \\lt \\beta \\lt \\dfrac{\\pi}{2}\\) , \\(0 \\lt \\gamma \\lt \\dfrac{\\pi}{2}\\) , \\(\\alpha +\\beta +\\gamma = \\dfrac{\\pi}{2}\\) \u3092\u6e80\u305f\u3059\u3068\u304d,\r\n\\[\r\n\\tan \\alpha \\tan \\beta +\\tan \\beta \\tan \\gamma +\\tan \\gamma \\tan \\alpha\r\n\\]\r\n\u306e\u5024\u306f\u4e00\u5b9a\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u5b9f\u6570 \\(\\alpha , \\beta , \\gamma\\) \u304c \\(0 \\lt \\alpha \\lt \\dfrac{\\pi}{2}\\) , \\(0 \\lt \\beta \\lt \\dfrac{\\pi}{2}\\) , \\(0 \\lt \\gamma \\lt \\dfrac{\\pi}{2}\\) , \\(\\alpha +\\beta +\\gamma = \\dfrac{\\pi}{2}\\) \u3092\u6e80\u305f\u3059\u3068\u304d,\r\n\\[\r\n\\tan \\alpha +\\tan \\beta +\\tan \\gamma\r\n\\]\r\n\u306e\u3068\u308a\u3046\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n

    \u6761\u4ef6\u3088\u308a\r\n\\[\r\n\\tan \\beta = \\dfrac{1}{\\tan \\alpha} = \\tan \\left( \\dfrac{\\pi}{2} -\\alpha \\right) \\ .\r\n\\]\r\n\\(0 \\lt \\alpha \\lt \\dfrac{\\pi}{2}\\) , \\(0 \\lt \\beta \\lt \\dfrac{\\pi}{2}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\beta & = \\dfrac{\\pi}{2} -\\alpha \\\\\r\n\\text{\u2234} \\quad \\alpha +\\beta & = \\underline{\\dfrac{\\pi}{2}} \\ .\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\(S = \\tan \\alpha \\tan \\beta +\\tan \\beta \\tan \\gamma +\\tan \\gamma \\tan \\alpha\\) \u3068\u304a\u304f.
    \r\n\u6761\u4ef6\u3088\u308a, \\(\\gamma = \\dfrac{\\pi}{2} -\\left( \\alpha +\\beta \\right)\\) \u306a\u306e\u3067, \u52a0\u6cd5\u5b9a\u7406\u3092\u7528\u3044\u3066\r\n\\[\r\n\\tan \\gamma = \\dfrac{1 -\\tan \\alpha \\tan \\beta}{\\tan \\alpha +\\tan \\beta} \\ .\r\n\\]\r\n\u3053\u308c\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nS & = \\tan \\alpha \\tan \\beta +\\left( \\tan \\alpha +\\tan \\beta \\right) \\dfrac{1 -\\tan \\alpha \\tan \\beta}{\\tan \\alpha +\\tan \\beta} \\\\\r\n& = 1 \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \\(S\\) \u306f\u4e00\u5b9a\u3067\u3042\u308b.<\/p>\r\n

    (3)<\/strong><\/p>\r\n

    \\(T = \\tan \\alpha +\\tan \\beta +\\tan \\gamma\\) , \\(U = \\tan^2 \\alpha +\\tan^2 \\beta +\\tan^2 \\gamma\\) \u3068\u304a\u304f.
    \r\n(2)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\left( \\tan \\alpha -\\tan \\beta \\right)^2 & +\\left( \\tan \\beta -\\tan \\gamma \\right)^2 +\\left( \\tan \\gamma -\\tan \\alpha \\right)^2 \\\\\r\n& = 2U -2S = 2U-2 \\geqq 0 \\\\\r\n\\text{\u2234} \\quad U & \\geqq 1 \\ .\r\n\\end{align}\\]\r\n\u3055\u3089\u306b, \u3053\u308c\u3092\u7528\u3044\u308c\u3070\r\n\\[\r\nT^2 = U +2S \\geqq 3 \\ .\r\n\\]\r\n\u6761\u4ef6\u3088\u308a, \\(T \\gt 0\\) \u306a\u306e\u3067\r\n\\[\r\nT \\geqq \\sqrt{3} \\quad ... [1] \\ .\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(\\tan \\alpha = \\tan \\beta = \\tan \\gamma\\) \u3059\u306a\u308f\u3061 \\(\\alpha = \\beta = \\gamma = \\dfrac{\\pi}{6}\\) \u306e\u3068\u304d.
    \r\n\u307e\u305f, \\(\\alpha \\rightarrow \\dfrac{\\pi}{2} -0\\) , \\(\\beta \\rightarrow +0\\) , \\(\\gamma \\rightarrow +0\\) \u306e\u3068\u304d\r\n\\[\r\nS \\rightarrow \\infty \\quad ... [2] \\ .\r\n\\]\r\n[1] [2] \u3088\u308a, \u6c42\u3081\u308b\u5024\u306e\u7bc4\u56f2\u306f\r\n\\[\r\n\\underline{S \\geqq \\sqrt{3}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u5404\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u5b9f\u6570 \\(\\alpha , \\beta\\) \u304c \\(0 \\lt \\alpha \\lt \\dfrac{\\pi}{2}\\) , \\(0 \\lt \\beta \\lt \\dfrac{\\pi}{2} … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[94],"tags":[145,111],"class_list":["post-836","post","type-post","status-publish","format-standard","hentry","category-ikashika_2013","tag-ikashika","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/836","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=836"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/836\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}