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MathGroup Archive 2004

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Re: Hyperbolic function identity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50942] Re: [mg50932] Hyperbolic function identity
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Tue, 28 Sep 2004 02:10:02 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 28 Sep 2004, at 13:58, Carlos Felippa wrote:

> Why
>
>    FullSimplify[ArcCosh[1+z^2/2]-2*ArcSinh[z/2],z>0];
>
> does not evaluate to 0?
>
>

This works.


FullSimplify[TrigToExp[ArcCosh[1 + z^2/2] - 2*ArcSinh[z/2]], z > 0]

0

I think TrigToExp is already among the functions that  FullSimplify 
uses and indeed this does not help:


FullSimplify[ArcCosh[1 + z^2/2] - 2*ArcSinh[z/2], z > 0,
   TransformationFunctions -> {Automatic, TrigToExp}]

ArcCosh[z^2/2 + 1] - 2*ArcSinh[z/2]

However, this again works:


Simplify[ArcCosh[1+z^2/2]-2*ArcSinh[z/
         2],z>0,TransformationFunctions->{Automatic,
     FullSimplify[TrigToExp[#],z>0]&}]

0


Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/


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