Re: How to simplify ArcSin formula
- To: mathgroup at smc.vnet.net
- Subject: [mg123303] Re: How to simplify ArcSin formula
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 1 Dec 2011 05:49:19 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201111301205.HAA19862@smc.vnet.net>
You are making several assumptions which hide the actual complexity of the situation. The expression is only zero for a certain range of parameter values, as can be clearly seen from this graph: Plot3D[Chop[ t + ArcSin[aa] - ArcSin[aa Cos[t] + Sqrt[1 - aa^2] Sin[t]]], {t, -Pi/2, Pi/2}, {aa, -1, 1}, AxesLabel -> {"t", "aa", "x"}] Andrzej Kozlowski On 30 Nov 2011, at 13:05, Alexei Boulbitch wrote: > 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> > > > > > > > > > > >