# Double Angle Formulas/Cosine/Proof 2

$\cos 2 \theta = \cos^2 \theta - \sin^2 \theta$
 $\displaystyle \cos 2 \theta$ $=$ $\displaystyle \map \cos {\theta + \theta}$ $\displaystyle$ $=$ $\displaystyle \cos \theta \cos \theta - \sin \theta \sin \theta$ Cosine of Sum $\displaystyle$ $=$ $\displaystyle \cos^2 \theta - \sin^2 \theta$
$\blacksquare$