Solve $\cosh x=\cos(a)$

Question

If we have $a$ is a real number. I know that the solution of $\cosh x=0$ is $x=2n\pi i+i\pi$. But how we can solve $\cosh x=\cos(a)$ to find $x$?

Answer 1

$\cos(a)=\frac{\exp(ia)+\exp(-ia)}2=\cosh(ia)$

Similary, $\cos(a)=\cos(2k\pi\pm a)=\cosh(i(2k\pi\pm a))$