How to simplify sin^2x/(cos^2+3cosx+2)=(1-cosx)/(2+cosx)sin2xcos2+3cosx+2=1cosx2+cosx?

(Sin^2X)/(cos^2x+3cosX+2)=(1-cosX)/(2+cosx)sin2Xcos2x+3cosX+2=1cosX2+cosx

1 Answer
Feb 1, 2018

LHS=sin^2x/(cos^2x+3cosx+2)LHS=sin2xcos2x+3cosx+2

=sin^2x/(cos^2x+cosx+2cosx+2)=sin2xcos2x+cosx+2cosx+2

=(1-cos^2x)/((cosx(cosx+1)+2(cosx+1))=1cos2x(cosx(cosx+1)+2(cosx+1))

=((1-cosx)(1+cosx))/((cosx+1)(cosx+2))=(1cosx)(1+cosx)(cosx+1)(cosx+2)

=(1-cosx)/(2+cosx)=RHS=1cosx2+cosx=RHS