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Re: Simplification question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110379] Re: Simplification question
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Wed, 16 Jun 2010 05:37:07 -0400 (EDT)
  • References: <hv76mt$k6e$1@smc.vnet.net>

Yaroslav Bulatov wrote:

> I'd like to verify that the following expression is true for a,b real.
> It seems to hold numerically.
>
> 1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] ==
> ArcTanh[Tanh[a] Tanh[b]]
>
> I tried Reduce and combinations of TrigToExp/Simplify with no luck,
> any suggestions?
>

At least for Reals you can verify it:

1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] == 
   ArcTanh[Tanh[a] Tanh[b]] // TrigToExp // 
 FullSimplify[#, {a, b} \[Element] Reals] &

 
//Peter
-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de


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