use the fact that $\tan 2x=\sin2x \ /\cos2x$ to prove that $\tan 2x=2\tan x/(1-\tan^2x)$

I need to use the fact that $\tan 2x=\sin2x \ /\cos2x$ to prove that: $$\tan 2x=\frac{2\tan x}{1-\tan^2x}$$ I don't know where to start. Please help or hint. Thanks in advance.

Use the identities: $$\cos{(2x)}=\cos^2{(x)}-\sin^2{(x)}$$ and $$\sin{(2x)}=2\sin(x)\cos(x)$$
since you'll get: $$\frac{2\sin(x)\cos(x)}{\cos^2{(x)}-\sin^2{(x)}}$$ can you take it from there?