# Math Help - Next step on proving an identity.

1. ## Next step on proving an identity.

Hello. I'm trying to prove:

$cot(\frac{A}{2}) - tan(\frac{A}{2}) = 2 cot (A)$

So far, this is what I've done:

$cot(\frac{A}{2}) - tan(\frac{A}{2}) = \dfrac{1+cos(A)+cos(A)+cos^2(A)-sin^2(A)}{sin(A)(1+cos(A))}$

If it weren't for the pesky $cos^2(A)-sin^2(A)$, I could simplify the numerator pretty easily. However, that not being the case, I'm not sure what the next step is.

Thanks.

2. 1+2cos(a)+cos^2(a)-(1-cos^2(a))=2cos(a)+2cos^2(a)=...

3. Thanks, that got me where I needed to go!