：求证:(cos^2x-sin^2x)(cos^4x+sin^4x)+1/4sin2xsin4x=cos2x求证:(cos^2x-_数学解答

：求证:(cos^2x-sin^2x)(cos^4x+sin^4x)+1/4sin2xsin4x=cos2x
求证:(cos^2x-sin^2x)(cos^4x+sin^4x)+1/4sin2xsin4x=cos2x
我算到右边=cos2x（1-sin^2xcos^2x）接下来该怎么办?

人气：488 ℃　时间：2019-10-31 12:04:46

解答

不知道你怎么算的
左边=cos2x[(sin²x+cos²x)²-2sin²xcos²x]+1/4sin2x*2sin2xcos2x
=cos2x[1-1/2*(2sinxcosx)²]+1/2sin²2xcos2x
=cos2x-1/2*sin²2xcos2x+1/2sin²2xcos2x
=cos2x