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/