# Cosine of 75 Degrees

## Theorem

$\cos 75^\circ = \cos \dfrac {5 \pi}{12} = \dfrac {\sqrt 6 - \sqrt 2} 4$

where $\cos$ denotes the cosine.

## Proof

 $\displaystyle \cos 75^\circ$ $=$ $\displaystyle \cos \left({90^\circ - 15^\circ}\right)$ $\displaystyle$ $=$ $\displaystyle \sin 15^\circ$ Cosine of Complement equals Sine $\displaystyle$ $=$ $\displaystyle \dfrac {\sqrt 6 - \sqrt 2} 4$ Sine of $15^\circ$

$\blacksquare$