# Cos(x) = cosh(x)?

1. ### contempquant

13
1. The problem statement, all variables and given/known data

2. Relevant equations
from the identities found on the internet:

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

and

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

3. 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

2. ### Dick

25,887
It shows cosh(ix)=cos(x), not cosh(x)=cos(x). There's nothing wrong with that.