化简1/4sin2x·sin4x-sin^8x+cos^8x

来源：学生作业学帮网编辑：学帮网时间：2024/05/15 12:28:13

原式=(2sin^2(2x)cos2x)/4+（cos^4x+sin^4x）(cos^2x+sin^2x)(cos^2x-sin^2x)
=2sin^2xcos^2xcos2x+（cos^4x+sin^4x）cos2x
=cos2x（cos^4x+2sin^2xcos^2x+sin^4x）
=cos2x(cos^2x+sin^2x)^2
=cos2x