Riemann Surfaces of Inverses of Sums of Two Trigonometric Functions

The graphic shows some sheets of the Riemann surface of for inverses of sums of trigonometric functions and . For purely real or imaginary parts ( or ), multiple sheets can degenerate into a single sheet.
  • Contributed by: Michael Trott with permission of Springer
  • From: The Mathematica Guidebook for Programming, second edition by Michael Trott (© Springer, 2008).

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DETAILS

Closed-form representation of these inverse functions can be given (say by using in Mathematica), but they can be quite complicated.
For instance (in shortened form):

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