Answer
$\tan (x+\frac{\pi}{3})=\frac{\sqrt{3}+\tan x}{1-\sqrt{3}\tan x}$
Work Step by Step
Start with the left side:
$\tan (x+\frac{\pi}{3})$
Expand using the addition formula for tangent:
$=\frac{\tan x+\tan \frac{\pi}{3}}{1-\tan x\tan \frac{\pi}{3}}$
Evaluate $\tan \frac{\pi}{3}$:
$=\frac{\tan x+\sqrt{3}}{1-\tan x*\sqrt{3}}$
$=\frac{\sqrt{3}+\tan x}{1-\sqrt{3}\tan x}$
Since this equals the right side, the identity has been proven.
