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-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