Question

how do you prove cosh x + sinh x = e^x

Answer 1

depends on your definition of \(\cosh(x)\) and \(\sinh(x)\)
they are usually defined in terms of \(e^x\) and all you would do in that case is add

Answer 2

\[
\cosh(x) = \frac{e^x+e^{-x}}{2}
\]

Answer 3

\[
\sinh(x) = \frac{e^x-e^{-x}}{2}
\]

Answer 4

I would just try adding them: =)