# Tangent of Angle plus Straight Angle

## Theorem

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

## Proof

 $\displaystyle \tan \left({x + \pi}\right)$ $=$ $\displaystyle \frac {\sin \left({x + \pi}\right)} {\cos \left({x + \pi}\right)}$ Tangent is Sine divided by Cosine $\displaystyle$ $=$ $\displaystyle \frac {-\sin x} {-\cos x}$ Sine of Angle plus Straight Angle and Cosine of Angle plus Straight Angle $\displaystyle$ $=$ $\displaystyle \tan x$ Tangent is Sine divided by Cosine

$\blacksquare$