# How do you simplify tan(x+pi)?

Mar 30, 2018

This simplifies to $\tan x$

#### Explanation:

We use the addition formula for tangent, $\tan \left(A + B\right) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$, and the fact that $\tan \left(\pi\right) = \frac{0}{1} = 0$.

Therefore:

$\tan \left(x + \pi\right) = \frac{\tan x + \tan \left(\pi\right)}{1 - \tan x \tan \left(\pi\right)} = \frac{\tan x + 0}{1 - 0} = \tan x$

Hopefully this helps!