化简 cos8次方x减sin8次方x+1/4sin2xsin4x
问题描述：
化简 cos8次方x减sin8次方x+1/4sin2xsin4x
答
cos^8x-sin^8x+1/4sin2x sin4x
=(cos^4x+sin^4x)(cos^4x-sin^4x)+1/2sin^22xcos2x
=(cos^4x+sin^4x)(cos^2x-sin^2x)+2sin^2xcos^2x(cos^2x-sin^2x)
=cos^6x-sin^6x+sin^2xcos^4x-sin^4xcos^2x
=cos^4x-sin^4x
=cos^2x-sin^2x
=cos2x