# Tangent of 165 Degrees

## Theorem

$\tan 165^\circ = \tan \dfrac {11 \pi} {12} = - \left({2 - \sqrt 3}\right)$

where $\tan$ denotes tangent.

## Proof

 $\displaystyle \tan 165^\circ$ $=$ $\displaystyle \tan \left({90^\circ + 75^\circ}\right)$ $\displaystyle$ $=$ $\displaystyle - \cot 75^\circ$ Tangent of Angle plus Right Angle $\displaystyle$ $=$ $\displaystyle - \left({2 - \sqrt 3}\right)$ Cotangent of $75^\circ$

$\blacksquare$