Double Angle Formulas/Hyperbolic Cosine/Corollary 1

Corollary to Double Angle Formula for Hyperbolic Cosine

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

where $\cosh$ denotes hyperbolic cosine.

Proof

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

$\blacksquare$