Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?
- To: mathgroup at smc.vnet.net
- Subject: [mg73520] Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?
- From: "Brian Gladman" <brg at nowhere.org>
- Date: Wed, 21 Feb 2007 01:41:16 -0500 (EST)
- References: <erelp9$7mm$1@smc.vnet.net>
"David W.Cantrell" <DWCantrell at sigmaxi.net> wrote in message news:erelp9$7mm$1 at smc.vnet.net... >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? I imagine that you would consider: Log[2 + Sqrt[5]]/(Log[Expand[((1 + Sqrt[5])/2)^3]]/3) to be cheating :-) Brian Gladman