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

• To: mathgroup at smc.vnet.net
• Subject: [mg73534] Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Wed, 21 Feb 2007 01:48:51 -0500 (EST)
• References: <erelp9\$7mm\$1@smc.vnet.net>

```On Feb 20, 1:24 pm, "David W.Cantrell" <DWCantr... 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

Not exactly what you want but I think it deserves to be mentioned

In[50]:=
FullSimplify[ArcSinh[2]/ArcCsch[2] - 3]

Out[50]=
0

Regards
Dimitris

```

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