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[?] Calculate a trigonometric function?

Jacques Ou
Posted 6 years ago

Please help me with calculating the following trigonometric function 

ArcTan[1/x] + ArcTan[x]]

Thanks.
POSTED BY: Jacques Ou
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Reduce[z == ArcTan[1/x] + ArcTan[x], {x}, Reals] gets you most of the way there.

This seems to do the trick:

PiecewiseExpand@Piecewise[
  Join @@ 
     With[{assum = And @@ Cases[#, Except[_Equal]]},
       ({z, assum} /. Solve[FullSimplify[#, assum]])] & /@ 
   List @@ LogicalExpand@
     Reduce[z == ArcTan[1/x] + ArcTan[x], {x}, Reals],
  Indeterminate]  (* <-- or Undefined *)
POSTED BY: Michael Rogers
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