Prove that cosh (-x) = cosh x

by RoRi

November 17, 2015

Prove that

$\cosh (-x) = \cosh x.$

Proof. We use the definition of the hyperbolic cosine,

$\begin{align*} \cosh (-x) &= \frac{e^{-x} + e^x}{2} \\ &= \frac{e^x + e^{-x}}{2} \\ &= \cosh x. \qquad \blacksquare \end{align*}$

Stumbling Robot