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Re: Simplification question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110402] Re: Simplification question
  • From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
  • Date: Wed, 16 Jun 2010 05:41:33 -0400 (EDT)

FullSimplify[(
 1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])])/
 ArcTanh[Tanh[a] Tanh[b]]
 , Assumptions -> {a > 0 && b > 0}]

1

FullSimplify[
 1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] - 
  ArcTanh[Tanh[a] Tanh[b]]
 , Assumptions -> {a > 0 && b > 0}]

0

??





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?


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