三角函数一题,(cosx)^8-(sinx)^8+1/4sin2xsin4x

问题描述:

三角函数一题,(cosx)^8-(sinx)^8+1/4sin2xsin4x

原式=(cos²x-sin²x)(cos²x+sin²x)[(cos²x+sin²x)²-2(sinxcosx)²]+(1/2)sin²2xcos2x
=cos2x-(1/2)cos2xsin²2x+(1/2)cos2xsin²2x
=cos2x