I don't see a simple way of answering this question but a more tractable approach might be to just use the complex inverse cosine function: Inverse trigonometric functions - Wikipedia, the free encyclopedia (logarithmic forms).
Q: Solve for .
My attempt:
Let . Then
be definition
and
So, I have to solve
and
I am not familiar with hyperbolic sine and cosine, so I am not sure what identities I can use. Is there are way to solve without using trig inverses and identities? I would think so, because our text didn't cover any examples like this.
I don't see a simple way of answering this question but a more tractable approach might be to just use the complex inverse cosine function: Inverse trigonometric functions - Wikipedia, the free encyclopedia (logarithmic forms).