Double Angle Formula for 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

\(\ds \cos 2 \theta\) \(=\) \(\ds \cos^2 \theta - \sin^2 \theta\) 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.


Also see


Sources