Mathematica supports hyperbolic functions everywhere in the complex plane—with careful attention to branch cuts—and provides an extensive web of exact and algebraic transformations, together with efficient arbitrary-precision numerical evaluation.
FullSimplify — simplify hyperbolic function expressions
FunctionExpand — reduce to algebraic forms or simpler arguments
TrigToExp,
ExpToTrig — convert between hyperbolic and exponential functions
ComplexExpand — expand into real and imaginary parts
