# Double Angle Formulas/Hyperbolic Cosine/Corollary 2

## 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 $\displaystyle$ $=$ $\displaystyle 1 + 2 \sinh^2 x$

$\blacksquare$