# How do you simplify ( 1+ tanx) /( 1- tanx)?

May 19, 2016

$\frac{1 + \tan x}{1 - \tan x} = \tan \left(x + \frac{\pi}{4}\right)$

#### Explanation:

We know that $\tan \left(A + B\right) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$ and $\tan \left(\frac{\pi}{4}\right) = 1$

Hence $\frac{1 + \tan x}{1 - \tan x}$

= (tan(pi/4)+tanx)/(1-tan(pi/4)tanx, as $\tan \left(\frac{\pi}{4}\right) = 1$

= $\tan \left(x + \frac{\pi}{4}\right)$