Verify if 1 -sin^2x/(1+cos x)=cos x?
We'll keep 1 to the left side and we'll move the fraction (sin x)^2/(1+cos x) to the right side:
cos x + (sin x)^2/(1+cos x) = 1
We'll multiply both sides by 1 + cos x:
cos x*(1+cos x) + (sin x)^2 = 1 + cos x
We'll remove the brackets:
cos x + (cos x)^2 + (sin x)^2 = 1 + cos x
But, from Pythagorean identity, we'll get:
(cos x)^2 + (sin x)^2 = 1
The expression will become a equality:
cos x + 1 = 1 + cos x
Since the LHS is equal to RHS, the given identity 1 -sin^2x/(1+cos x)=cos x is verified.