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.