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Re: How to simplify ArcSin formula

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123286] Re: How to simplify ArcSin formula
  • From: Ray Koopman <koopman at sfu.ca>
  • Date: Wed, 30 Nov 2011 03:21:44 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <jb2hsp$5df$1@smc.vnet.net>

On Nov 29, 4:06 am, David Sagan <david.sa... at gmail.com> wrote:
> 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 [...]

It is ?

xxx = t + ArcSin[aa] - ArcSin[aa Cos[t] + Sqrt[1 - aa^2] Sin[t]];
xxx /. t -> Pi/2
% /. aa -> 1/2

Pi/2 + ArcSin[aa] - ArcSin[Sqrt[1 - aa^2]]
Pi/3



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