Is there any mechanism in Mathematica to simplify ArcTan[Tan[t]] to t? The functions Simplify and FullSimplify leave it as is. When trying to discover relationships, it is useful to consider the arc functions applied to the trig functions as the identity.

Incidentally, Simplify[Tan[ArcTan[t]]] evaluates to t.


You need an assumption

Simplify[ArcTan[Tan[t]], -π/2 < Re[t] < π/2]


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  • $\begingroup$ Ah! Thank you! ${}$ $\endgroup$ – Joseph O'Rourke Feb 7 '18 at 13:09
  • $\begingroup$ For what it's worth, in this case it also works without the Re - Simplify[ArcTan[Tan[t]], -π/2 < t < π/2] also works. $\endgroup$ – numbermaniac Jul 20 '18 at 1:38

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