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

• To: mathgroup at smc.vnet.net
• Subject: [mg73499] Showing that ArcSinh[2]/ArcCsch[2] is 3?
• From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
• Date: Tue, 20 Feb 2007 06:19:31 -0500 (EST)

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

• Follow-Ups:
  • Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?
    • From: János <janos.lobb@yale.edu>
  • Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>