Prove the trigonometric identity $\cos(x) + \sin(x)\tan(\frac{x}{2}) = 1$ While solving an equation i came up with the identity $\cos(x) + \sin(x)\tan(\frac{x}{2}) = 1$.
Prove whether this is really true or not. I can add that $$\tan\left(\frac{x}{2}\right) = \sqrt{\frac{1-\cos x}{1+\cos x}}$$

$ t = \tan(../2) $
$$ \sin ( ..) = \frac{ 2 t }{1+t^2}  ; \,  \cos ( ..) = \frac{ 1-t^2 }
{1+t^2} $$
Plug in
$$\cos x+\sin x\tan \frac{x}{2} \rightarrow 1 $$
