# Double Angle Formulas/Cosine/Corollary 2

## Corollary to Double Angle Formula for Cosine

$\cos 2 \theta = 1 - 2 \sin^2 \theta$

where $\cos$ and $\sin$ denote cosine and sine respectively.

## Proof

 $\displaystyle \cos 2 \theta$ $=$ $\displaystyle \cos^2 \theta - \sin^2 \theta$ Double Angle Formula for Cosine $\displaystyle$ $=$ $\displaystyle \left({1 - \sin^2 \theta}\right) - \sin^2 \theta$ Sum of Squares of Sine and Cosine $\displaystyle$ $=$ $\displaystyle 1 - 2 \sin^2 \theta$

$\blacksquare$