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>