Prove that cosh x + sinh x = e^x

by RoRi

November 18, 2015

Prove that

$\cosh x + \sinh x = e^x.$

Proof. We use the definitions of hyperoblic sine and cosine to compute,

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

Stumbling Robot

Prove that cosh x + sinh x = e^x

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