Power Reduction Formulas/Cosine Squared/Proof 1

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Theorem

$\cos^2 x = \dfrac {1 + \cos 2 x} 2$


Proof

\(\displaystyle 2 \cos^2 x - 1\) \(=\) \(\displaystyle \cos 2 x\) Double Angle Formula for Cosine: Corollary 1
\(\displaystyle \cos^2 x\) \(=\) \(\displaystyle \frac {1 + \cos 2 x} 2\) solving for $\cos^2 x$

$\blacksquare$