How Are Cos(x) and Cosh(x) Related in Mathematical Identities?

[contempquant]

Homework Statement

Homework Equations

from the identities found on the internet:

cos(x)=\frac{(e^{ix}+e^{-ix})}{2}

and

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

The Attempt at a Solution

Assuming for the definition of cosh(x), if we take x as being equal to (ix), then surely this shows that cosh(x)=cos(x)? Can someone explain why this is wrong please? because i can't see it

 

[Dick]

It shows cosh(ix)=cos(x), not cosh(x)=cos(x). There's nothing wrong with that.