Prove that sinh(2x) = 2 sinh x cosh x

by RoRi

November 17, 2015

Prove that

$\sinh (2x) = 2 \sinh x \cosh x.$

Proof. We know from this exercise (Section 6.19, Exercise #5) that

$\sinh (x+y) = \sinh x \cosh x + \cosh x \sinh y.$

Therefore,

$\begin{align*} \sinh (2x) &= \sinh (x+x) \\ &= \sinh x \cosh x + \cosh x \sinh x \\ & = 2 \sinh x \cosh x. \qquad \blacksquare \end{align*}$

Stumbling Robot