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.
Solution 1:
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?