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Re: How to simplify ArcSin formula

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123285] Re: How to simplify ArcSin formula
  • From: Dana DeLouis <dana01 at me.com>
  • Date: Wed, 30 Nov 2011 03:21:33 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

> The answer I know is xxx = 0...

I don't believe it's true for all cases of t.

aa=1/2;

xxx = t+ArcSin[aa]-ArcSin[aa Cos[t]+Sqrt[1-aa^2] Sin[t]];

Maybe for a small range...

xxx/. t->1.   //Chop
0

However...

xxx/. t->2.
1.9056

xxx/. t->3.
3.9056

xxx/. t->4.
5.9056

= = = = = = = = = = 
HTH
Dana DeLouis
= = = = = = = = = = 


On Nov 29, 7:06 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 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





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