Упростите выражение cosx+sin2x-cos3x

cosx+sin2x-cos3x=cosx+2sinxcosx-cos (2x+x)=cosx+2sinxcosx- (cos2x*cosx-sin2x*sinx)=cosx+2sinxcosx-cos2x*cosx+sin2x*sinx=cosx+2sinxcosx- (cos^2x-sin^2x)*cosx+2sin^2x*cosx=cosx+2sinxcosx-cos^3x+sin^2x*cosx+2sin^2x*cosx=cosx+2sinxcosx-cos^3x+3sin^2x*cosx=cosx (1+2sinx-cos^2x+3sin^2x)=cosx (sin^2x+2sinx+3sin^2x)=cosx (4sin^2x+2sinx)=2sinxcosx*(sinx+1)=sin2x*sinx+sin2x