Hello

Could someone please help me start with proving the following identity:

$\displaystyle \tan \dfrac{A}{2} + \cot \dfrac{A}{2} \equiv 2\csc A$

I'm trying to show that the L.H.S = the R.H.S. I've tried finding the half angle formula for $\displaystyle \tan \dfrac{A}{2}$, but it looks like a quadratic. I have also tried writing the L.H.S as a single term. I'm totally stuck. A hint would be greatly appreciated.

Thank you