Double Angle Formulas/Hyperbolic Cosine/Corollary 1

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Corollary to Double Angle Formula for Hyperbolic Cosine

$\cosh 2 x = 2 \cosh^2 x - 1$

where $\cosh$ denotes hyperbolic cosine.


Proof

\(\displaystyle \cosh 2 x\) \(=\) \(\displaystyle \cosh^2 x + \sinh^2 x\) Double Angle Formula for Hyperbolic Cosine
\(\displaystyle \) \(=\) \(\displaystyle \cosh^2 x + \left({\cosh^2 x - 1}\right)\) Difference of Squares of Hyperbolic Cosine and Sine
\(\displaystyle \) \(=\) \(\displaystyle 2 \ \cosh^2 x - 1\)

$\blacksquare$


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