Question

Упростите выражение cosx+sin2x-cos3x

Answer 1

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