Prove that cosh x – sinh x = e^-x

by RoRi

November 18, 2015

Prove that

$\cosh x - \sin x = e^{-x}.$

Proof. Using the definition of the hyperbolic functions in terms of the exponential, we have

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

2 comments

January 14, 2021 at 5:23 pm

Anonymous says:

y = mx+b

Reply
September 2, 2020 at 10:52 am

Anonymous says:

y=3x+1

Reply

Stumbling Robot

Prove that cosh x – sinh x = e^-x

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