问题 解答题
求证:cosx•cos2x•cos4x=
sin8x
8sinx
答案

证明:由倍角公式sin2x=2sinxcosx,

故sin8x=2sin4xcos4x=4sin2xcos2xcos4x=8sinxcosxcos2xcos4x,

所以

sin8x
8sinx
.=
8sinxcosxcos2xcos4x
8sinx
=cosx•cos2x•cos4x,

cosx•cos2x•cos4x=

sin8x
8sinx
.得证.

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