system
Given the following post, respond as if you're commenting on Reddit:
human
How does cosh(x) = cos(ix)?

We learned about the hyperbolic trig functions in Calc 2 recently, I looked up coshx in Wolfram Alpha and got cos(ix) as an alternate form. I asked my professor and he didn't really explain it other than saying it's higher mathematics.
gpt
One way to define the functions is as

cosh(x) = (e^(x) + e^(-x))/2

and

cos(x) = (e^(ix) + e^(-ix))/2

which makes that identity very clear. You can justify that these definition match with our other understandings of trigonometric functions by considering the Taylor series.