Prove: ((cot^2x)/(1+cot^2x)) = cos^2x

So unfortunate..proofs. please help!

1 + cot^2 x = csc^2 x

(cos^2 x/sin^2 x)/(1/sin^2 x) = (cos^2 x/sin^2 x) * (sin^2x / 1)

The sin^2 x terms cancel leaving only cos^2 x.