全文
[ 東京工業大学 1990 年後期 ２ ]
nを2以上の整数とする。
(1) n1次多項式Pn( )x とn次多項式Qn( )x ですべての実数に対して
sin(2n)nsin(2 ) Pn(sin2)
cos(2n)Qn(sin2)
を満たすものが存在することを帰納法を用いて表せ。
(2) k1, 2,,n1に対して
2
sin 2
k
k n
とおくと，
1 2 1
( ) (1 )(1 ) (1 )
n x x x n x
P となることを示せ。
(3)
1 2
1
2 2
3
n k k
n
を示せ。
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