# Double Angle Formulas/Cosine/Corollary 1

## Corollary to Double Angle Formula for Cosine

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

where $\cos$ denotes cosine.

## Proof

 $\ds \cos 2 \theta$ $=$ $\ds \cos^2 \theta - \sin^2 \theta$ Double Angle Formula for Cosine $\ds$ $=$ $\ds \cos^2 \theta - \paren {1 - \cos^2 \theta}$ Sum of Squares of Sine and Cosine $\ds$ $=$ $\ds 2 \cos^2 \theta - 1$

$\blacksquare$

## Also known as

This identity and Corollary $2$ are sometimes known as Carnot's Formulas, for Lazare Nicolas Marguerite Carnot.