# Secant of 105 Degrees

## Theorem

$\sec 105^\circ = \sec \dfrac {7 \pi} {12} = - \left({\sqrt 6 + \sqrt 2}\right)$

where $\sec$ denotes secant.

## Proof

 $\displaystyle \sec 105^\circ$ $=$ $\displaystyle \sec \left({90^\circ + 15^\circ}\right)$ $\displaystyle$ $=$ $\displaystyle - \csc 15^\circ$ Secant of Angle plus Right Angle $\displaystyle$ $=$ $\displaystyle - \left({\sqrt 6 + \sqrt 2}\right)$ Cosecant of 15 Degrees

$\blacksquare$