Double Angle Formulas/Hyperbolic Cosine/Corollary 2

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Corollary to Double Angle Formula for Hyperbolic Cosine

$\cosh 2 x = 1 + 2 \sinh^2 x$

where $\cosh$ and $\sinh$ denote hyperbolic cosine and hyperbolic sine respectively.


Proof

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

$\blacksquare$


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