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 $$\tan\left(\frac{x}{2}\right) = \sqrt{\frac{1-\cos x}{1+\cos x}}$$

An easy way to do that is:
sinx = sqrt((1+cosx)(1-cosx))
so LHS becomes:
cosx + sqrt((1+cosx)(1-sinx))sqrt((1-cosx)/1+cosx))
cosx + 1 - cosx = 1 = RHS
