I think it's pretty easy question, maybe even dumb one, but still I can't find a nice way to solve it.
How do you prove that $\forall x . \cosh(x) \ge 1$ , without using the identity: $\cosh^2x-\sinh^2x=1$, and not without using derivatives.
the defenition of $\cosh(x)$ is: $\frac{e^x+e^{-x} }{2}$
I already proved that using the identity, but I'm just wondering if there is another way. sadly, I couldn't find a proof using the search engine, even though that is a very basic question.
would appreciate your help!