Double Angle Formulas/Cosine/Corollary 2

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Corollary to Double Angle Formula for Cosine

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

where $\cos$ and $\sin$ denote cosine and sine respectively.


Proof

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

$\blacksquare$


Also see


Sources