问题标题：
求证!cos^8x-sin^8x+1/4sin2xsin4x=cos2x求数学大神帮忙详细过程谢谢
问题描述：
求证!cos^8x-sin^8x+1/4sin2xsin4x=cos2x
求数学大神帮忙详细过程谢谢
郎一民回答：
cos^8x-sin^8x+1/4sin2xsin4x-cos2x
=(cos^4x+sin^4x)(cos^4x-sin^4x)+1/2sin²2xcos2x-cos2x
=(cos^4x+sin^4x)(cos²x-sin²x)+2sin²xcos²x(cos²x-sin²x)-cos2x
=cos^6x-sin^6x+sin²xcos^4x-sin^4xcos²x-cos2x
=cos^4x-sin^4x-cos2x
=cos²x-sin²x-cos2x
=cos2x-cos2x
=0
所以cos^8x-sin^8x+1/4sin2xsin4x-cos2x=0
cos^8x-sin^8x+1/4sin2xsin4x=cos2x
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