Verified answer

Since sin^2θ + cos^2θ = 1, we see that:

sin^2θ = 1 - cos^2θ, by solving for sin^2θ.

So, substituting in sin^2θ for 1 - cos^2θ yields:

(1 - cos^2θ)/(1 + cos^2θ) = sin^2θ/(1 + cos^2θ).

I hope this helps!

There are some other ways to put it listed if you scroll down to alternative forms.

http://www.wolframalpha.com/input/?i=%281-cos%C2%B...

(1 - cos²(θ))/(1 + cos²(θ)) = (sin²(θ))/(2 - sin²(θ))