Prove the Identity: $\cosh(-x) = \cosh(x)$

Question

I am trying to prove this identity in my Calculus 1 class. Here is what I've got so far:

$\cosh(-x) = \cosh(x)$

$\cosh(-x) = \frac{1}{2}(e^{-x} + e^{-{(-x)}})$

$\cosh(-x)= \frac{1}{2}(e^{-x} + e^x)$

Any input is much appreciated.

Answer 1

You are almost there.

$\cosh(-x)= \frac{1}{2}(e^{-x} + e^x) = \frac{1}{2}(e^x + e^{-x} )$ (commutative property)

And the RHS is the definition of $\cosh(x)$