Prove the identity cot A/2 - tan A/2 = 2cot A

I have written it as:

$\displaystyle \frac{cos \frac{A}{2}}{sin \frac{A}{2}} - \frac { sin \frac {A}{2}}{cos \frac{A}{2}}$

Taking LCM:

$\displaystyle \frac {cos^2 \frac{A}{2} - sin^2 \frac{A}{2}}{sin \frac{A}{2} cos \frac{A}{2}} $

Now I don't know how to solve it any further?

Is there any easier method of proving this identity ?