This is probably pretty simple, I cant figure it out though.

"Prove the identity (T = Theta): (cos(2T)) / (1 + sin(2T)) = (cot(T) - 1) / (cot(T) + 1)"

So...

((cos(T)^2) - (sin(T)^2)) / (1 + 2*sin(T)*cos(T)) = (cos(T) - sin(T)) / (cos(T) + sin(T))

(cos(T) + sin(T)) * ((cos(T)^2) - (sin(T)^2)) = (cos(T) - sin(T)) * (1 + 2*sin(T)*cos(T))

(cos(T) + sin(T)) * (cos(T) - sin(T)) = (1 + 2*sin(T)*cos(T))

((cos(T)^2) - (sin(T)^2)) = (1 + 2*sin(T)*cos(T))

At this point I am stuck. What do I need to do now?