Question

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

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

Answer 1

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

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

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

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

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