Double Angle Formulas/Cosine/Corollary 1

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Corollary to Double Angle Formula for Cosine

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

where $\cos$ denotes cosine.


Proof

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

$\blacksquare$


Also see


Sources