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

• To: mathgroup at smc.vnet.net
• Subject: [mg73550] Re: Showing that ArcSinh[2]/ArcCsch[2] is 3?
• From: "sashap" <pavlyk at gmail.com>
• Date: Wed, 21 Feb 2007 06:03:54 -0500 (EST)
• References: <erelp9$7mm$1@smc.vnet.net>

Dear David,

It is the case in the CAS and in the real life as well that proving
left hand side equal to right hand side is easier than deriving
what right hand side the left hand side equals to.

I can not think of a direct way to use built-in 'knowledge' to reduce
ArcSinh[2]/ArcCsch[2] to 3, but want to point out that proving it
post-factum does not seem problematic:

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

Out[3]=
0

Sincerely,

Oleksandr Pavlyk
Special Functions Developer
Wolfram Research Inc

On Feb 20, 5:24 am, "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