求证sin3xsin^3x+cos3xcos^3x=cos^3 2x 求详解

显示全部楼层 · 2013-3-31 13:59:12

证明：左侧=sin(x+2x)sin^3x+cos(x+2x)cos^3x
=sin^4xcos2x+sin2xcosxsin^3x+cos^4xcos2x-sinxcos^3xsin2x
=sin^4xcos2x+2sin^4xcos^2x+cos^4xcos2x-2sin^2xcos^4x
=cos2x(sin^4x+cos^4x)+2sin^2xcos^2x(sin^2x-cos^2x)
=cos2x(sin^4x+cos^4x-2sin^2xcos^2x)
=cos2x(sin^2x-cos^2x)^2
=cos^3(2x)
=右侧所以sin3xsin^3x+cos...

千问 · 2013-3-31 13:59:12

sin3xsin^3x+cos3xcos^3x=cos^3(2x)证明：左侧=sin(x+2x)sin^3x+cos(x+2x)cos^3x
=sin^4xcos2x+sin2xcosxsin^3x+cos^4xcos2x-sinxcos^3xsin2x
=sin^4xcos2x+2sin^4xcos^2x+cos^4xcos2x...