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

Question

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

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Answer 1 · 2018-02-01T23:30:08

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

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

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

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

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