化简1/4sin2x·sin4x-sin^8x+cos^8x

来源：学生作业帮助网编辑：六六作业网时间：2024/12/19 02:40:48

化简1/4sin2x·sin4x-sin^8x+cos^8x化简1/4sin2x·sin4x-sin^8x+cos^8x化简1/4sin2x·sin4x-sin^8x+cos^8x原式=(2sin^2

化简1/4sin2x·sin4x-sin^8x+cos^8x
化简1/4sin2x·sin4x-sin^8x+cos^8x

化简1/4sin2x·sin4x-sin^8x+cos^8x
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