Double Angle Formulas/Cosine/Proof 2

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Theorem

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


Proof

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

$\blacksquare$