Re: Hyperbolic function identity
- To: mathgroup at smc.vnet.net
- Subject: [mg50944] Re: [mg50932] Hyperbolic function identity
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Wed, 29 Sep 2004 03:15:06 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
This also works
FullSimplify[ComplexExpand[ArcCosh[1 + z^2/2] - 2*ArcSinh[z/2]], z > 0]
0
However, it essentially amounts to the same thing as using TrigToExp.
Andrzej
On 28 Sep 2004, at 15:07, Andrzej Kozlowski wrote:
>
> On 28 Sep 2004, at 13:58, Carlos Felippa wrote:
>
>> *This message was transferred with a trial version of CommuniGate(tm)
>> Pro*
>> 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/
>