How do you prove sin^2x/ (cos^2 +3cosx+2) = (1-cosx)/ (2+cosx)?

See proof in explanation.
##(sin^2 x)/(cos^2 x + 3cosx + 2) =(1-cosx)/(2+cos x) ##
Start with the left hand side:
##(1-cos^2 x)/((cos x+1)(cos x + 2)) ##
##implies ((1-cos x)(1+cos x))/((cos x+1)(cos x + 2)) =(1-cosx)/(2+cos x) ##