2(sin^6x+cos^6)-3(sin^4x+cos^4x)
问题描述：
2(sin^6x+cos^6)-3(sin^4x+cos^4x)
答
sin^6x+cos^6x=(sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x)
=sin^4x-sin^2xcos^2x+cos^4x
=(sin^2x+cos^2x)^2-3sin^2xcos^2x
=1-3sin^2xcos^2x
sin^4x+cos^4x=(sin^2x+cos^2x)^2-2sin^2xcos^2x
=1--2sin^2xcos^2x
2(sin^6x+cos^6)-3(sin^4x+cos^4x)=2(1-3sin^2xcos^2x)-3(1--2sin^2xcos^2x)
=-1