# How do you prove the identity tan (x-pi/4)= (tan x - 1)/(1 + tan x)?

$\tan \left(\alpha - \beta\right) = \frac{\tan \alpha - \tan \beta}{1 + \tan \alpha \tan \beta}$,
$\tan \left(x - \frac{\pi}{4}\right) = \frac{\tan x - \tan \left(\frac{\pi}{4}\right)}{1 + \tan x \tan \left(\frac{\pi}{4}\right)} = \frac{\tan x - 1}{1 + \tan x}$
and this is because $\tan \left(\frac{\pi}{4}\right) = 1$.