Proof of tangent half identity 
Prove the following: $$\tan \left(\frac{x}{2}\right) = \frac{1 + \sin (x) - \cos (x)}{1 + \sin (x) + \cos (x)}$$

I was unable to find any proofs of the above formula online. Thanks!

Hints:


*

*$\sin x = 2 \sin \frac{x}{2} \cos \frac{x}{2}$

*$1 - \cos x = 2 \sin^2 \frac{x}{2}$

*$1 + \cos x = 2 \cos^2 \frac{x}{2}$

