Prove that sinh(-x) = – sinh x.

by RoRi

November 17, 2015

Prove that

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

Proof. We use the definition of the hyperbolic sine,

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

Stumbling Robot