# Improve FullSimplify/ExpToTrig

For $\frac{2 e^4}{e^8+1}$ function ExpToTrig returns

(* (2 (Cosh[4] + Sinh[4]))/(1 + Cosh[8] + Sinh[8]) *)


which is correct, but if I use Simplify/FullSimplify, I'll receive input value $\frac{2 e^4}{e^8+1}$ instead of obvious $\frac{1}{\cosh (4)}$ or $sech (4)$. However, It works perfectly with $\frac{e^8+1}{2 e^4}$

(* Cosh[4] *)

• The brute force workaround is 2 E^4/(E^8 + 1) // (1/# &) // FullSimplify // (1/# &) – Bob Hanlon May 7 '17 at 12:29
• Your solution is good, but needs generalization, because it won't work if you add one or more terms, for example x + 2 E^4/(E^8 + 1) // (1/# &) // FullSimplify // (1/# &) – xhF731 May 7 '17 at 12:49
• Please don't add bugs tag to the question until the community/WRI has confirmed it. – xzczd May 7 '17 at 12:53
• OK, sorry for that. – xhF731 May 7 '17 at 12:55

simplify[expr_] := 1/FullSimplify[1/expr]

expr1 = 2 E^4/(E^8 + 1);

expr1 // simplify

(*  Sech[4]  *)

expr2 = a + expr1;

simplify /@ expr2

(*  a + Sech[4]  *)