\\(\\theta\\) \u3092\u5b9f\u6570\u3068\u3057, \u6570\u5217 \\(\\{ a_n \\}\\) \u3092\r\n\\[\r\na_1 = 1 , \\quad a_2 = \\cos \\theta , \\quad a _{n+2} = \\dfrac{3}{2} a _{n+1} -a_n \\ ( n = 1, 2, 3, \\cdots )\r\n\\]\r\n\u306b\u3088\u308a\u5b9a\u3081\u308b. \u3059\u3079\u3066\u306e \\(n\\) \u306b\u3064\u3044\u3066 \\(a_n = \\cos (n-1) \\theta\\) \u304c\u6210\u308a\u7acb\u3064\u3068\u304d, \\(\\cos \\theta\\) \u3092\u6c42\u3081\u3088.<\/p>\r\n
\u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\n\\cos (n+1) \\theta & = \\dfrac{3}{2} \\cos n \\theta -\\cos (n-1) \\theta \\\\\r\n2 \\cos n \\theta \\cos \\theta & = \\dfrac{3}{2} \\cos n \\theta \\\\\r\n\\cos n \\theta \\left( \\cos \\theta -\\dfrac{3}{4} \\right) & = 0 \\\\\r\n\\text{\u2234} \\quad \\cos n \\theta = 0 & , \\ \\cos \\theta = \\dfrac{3}{4}\r\n\\end{align}\\]\r\n\\(\\cos n \\theta = 0\\) \u306e\u3068\u304d\u3092\u8003\u3048\u308b\u3068, \\(a_2 = a_3 = 0\\) \u3068\u306a\u308b\u304c\r\n\\[\r\na_1 = \\dfrac{3}{2} a_2 -a_3 = 0 \\neq 1\r\n\\]\r\n\u3067, \u77db\u76fe\u304c\u751f\u3058\u308b.
\r\n\u3088\u3063\u3066\r\n\\[\r\n\\cos \\theta = \\underline{\\dfrac{3}{4}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(\\theta\\) \u3092\u5b9f\u6570\u3068\u3057, \u6570\u5217 \\(\\{ a_n \\}\\) \u3092 \\[ a_1 = 1 , \\quad a_2 = \\cos \\theta , \\quad a _{n+2} = \\dfrac{3}{2} a _{ … \u7d9a\u304d\u3092\u8aad\u3080