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/ >