# Trouble with simplifying trigonometric / hyper-trigonometric functions

Why (correct) expressions like

Assuming[p > 0, 2 ArcTan[Sinh[p]] == Pi - 2 ArcTan[Csch[p]] // FullSimplify]


Are not correctly evaluated to: True? What is the best approach in these cases

• Note that the simpler expression Assuming[p > 0, 2 ArcTan[p] == Pi - 2 ArcTan[1/p] // FullSimplify] does evaluate to True. The problem seems to be that Mathematica doesn't recognize $\sinh x = 1/\mathrm{csch}\, x$ in this context. – Michael Seifert Mar 14 '19 at 13:57
• Series shows that the difference between the LHS and RHS is zero, i.e., Assuming[p > 0, Series[ 2 ArcTan[Sinh[p]] - (Pi - 2 ArcTan[Csch[p]]), {p, 0, 50}]] // Normal evaluates to 0 – Bob Hanlon Nov 14 '19 at 1:51

f[e_] := 100 Count[e, _Gudermannian | _Csch, {0, Infinity}] +