# How to simplify exponentials into hyperbolic functions

I have a function of real exponentials and I'd like to simplify it using hyperbolic functions. How can I tell mathematica to use $e^x +e^{-x}=2\cosh(x)$ when simplifying? (and obviusly the $\sinh$ relation too)

• FullSimplify? – Michael E2 May 1 '17 at 19:10
• I tried but it doesn't modify the exponentials – P. C. Spaniel May 1 '17 at 19:16
• It works for me. You probably need to show a typical use-case in which it fails. Backup plan: expr /. Power[E, x_] :> Cosh[x] + Sinh[x], which might simplify right back to exponentials if you're not careful. – Michael E2 May 1 '17 at 19:22
• ExpToTrig can be useful for this. – Daniel Lichtblau May 1 '17 at 19:22
• Make sure to use E^x not e^x. – kglr May 1 '17 at 19:31