I'am trying to prove the below identity, but this is what i end up getting. $\begin{align*} \frac{2\tan(x)}{1 + \tan^2(x)} &= \sin(2x)\\ &= \frac{2\frac{\sin(x)}{\cos(x)}}{1 + \frac{\sin^2(x)}{\cos^2(x)}}\\ &= 2\sin(x) \end{align*}$
Can someone point out the mistake for me please?