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How to simplify ArcSin formula

• To: mathgroup at smc.vnet.net
• Subject: [mg123249] How to simplify ArcSin formula
• From: David Sagan <david.sagan at gmail.com>
• Date: Tue, 29 Nov 2011 07:04:08 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I am trying to discover how to simplify xxx where xxx is defined to
be:
  xxx= t + ArcSin[aa] - ArcSin[aa Cos[t] + Sqrt[1 - aa^2] Sin[t]]
with
  -1 < aa < 1
The answer I know is xxx = 0 but the reason I am posing the question
is that I am interested in finding out, in general, how to manipulate
formulas of this type. I tried:
  FullSimplify[xxx, -1<a<1]
but that did not work. Can anyone tell me how to do this?

-- Thanks, David