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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

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    $\begingroup$ 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. $\endgroup$ – Michael Seifert Mar 14 at 13:57

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