Answer
$\tan (x-\frac{\pi}{4})=\frac{\tan x-1}{\tan x+1}$
Work Step by Step
Start with the left side:
$\tan (x-\frac{\pi}{4})$
Expand using the subtraction formula for tangent:
$=\frac{\tan x-\tan \frac{\pi}{4}}{1+\tan x\tan \frac{\pi}{4}}$
Evaluate $\tan \frac{\pi}{4}$:
$=\frac{\tan x-1}{1+\tan x*1}$
$=\frac{\tan x-1}{\tan x+1}$
Since this equals the right side, the identity has been proven.
