Solve the equation $1-\tan x + \tan^2 x - \tan^3 x + ... = \frac{\tan 2x}{1+\tan2x}$ How to solve this? Any advice?
$$1-\tan x + \tan^2 x - \tan^3 x + ... = \frac{\tan 2x}{1+\tan2x}$$
Next step I do this
$\sum\limits_{n=0}^\mathbb{\infty}(-1)^n  \tan^nx = \frac{\tan 2x}{1+\tan2x} $
But I don't know next step. I am culeless, thanks for any advice.

You have to put the restriction that the values of $|\tan x | <1$ for this to work. recall the formula for a sum of an infinite geometric series
