求证sin^4x-cos^4x=2sin^2x-1
问题描述：
求证sin^4x-cos^4x=2sin^2x-1
如果可以的话把tan^2x-sin^2x=tan^2xsin^2x帮求证一下
答
sin^4x-cos^4x=(sin^2x-cos^2x)(sin^2x+cos^2x)=sin^2x-cos^2x=2sin^2x-1 tan^2x-sin^2x=sin^2x/cos^2x-sin^2x=(sin2x-sin^2xcos^2x)/cos^2x=sin^4x/cos^2x=tan^2xsin^2x