       Re: How to simplify ArcSin formula

• To: mathgroup at smc.vnet.net
• Subject: [mg123297] Re: How to simplify ArcSin formula
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Wed, 30 Nov 2011 07:05:01 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi, David,

You should help Mathematica understanding what you would like to get. I would do it like follows:

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

xxx1 = xxx /. aa -> Sin[\[CurlyPhi]] /.

Sqrt[1 - Sin[\[Alpha]_]^2] -> Cos[\[Alpha]]

This gives you

t + ArcSin[Sin[\[CurlyPhi]]] -

ArcSin[Cos[\[CurlyPhi]] Sin[t] + Cos[t] Sin[\[CurlyPhi]]]

Then make

Simplify[xxx1] /. ArcSin[Sin[\[Alpha]_]] -> \[Alpha]

Giving you 0.

Have fun, Alexei

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

Alexei BOULBITCH, Dr., habil.

IEE S.A.

ZAE Weiergewan,

11, rue Edmond Reuter,

L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566

Office fax:       +352-2454-3566

mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu<mailto:alexei.boulbitch at iee.lu>

```

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