Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?

*To*: mathgroup at smc.vnet.net*Subject*: [mg73528] Re: [mg73499] Showing that ArcSinh[2]/ArcCsch[2] is 3?*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Wed, 21 Feb 2007 01:45:34 -0500 (EST)*Reply-to*: hanlonr at cox.net

expr=ArcSinh[2]/ArcCsch[2]; Rationalize[expr,10^-100] 3 Reduce[{ArcSinh[x]/ArcCsch[x]==3,x>0},x] x == 2 Off[N::meprec]; expr==3//FullSimplify True On[N::meprec]; Bob Hanlon ---- "David W.Cantrell" <DWCantrell at sigmaxi.net> wrote: > I hope I've just overlooked something very simple. > I want to transform ArcSinh[2]/ArcCsch[2] to 3, using just "knowledge" > already implemented in Mathematica. I tried FullSimplify first, and it > doesn't help. I tried several other things. For example, > > TrigToExp[ArcSinh[2]/ArcCsch[2]] yields > > Log[2 + Sqrt[5]]/Log[1/2 + Sqrt[5]/2]. > > But then how should we transform that to 3? > > David