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Re: Simplification question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110377] Re: Simplification question
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Wed, 16 Jun 2010 05:36:45 -0400 (EDT)

On 6/15/10 at 2:30 AM, yaroslavvb at gmail.com (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?

In[7]:= eq =
  1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] ==
   ArcTanh[Tanh[a] Tanh[b]];

In[8]:= Assuming[{a, b} \[Element] Reals, FullSimplify[TrigToExp[eq]]]

Out[8]= True

In[9]:= $Version

Out[9]= 7.0 for Mac OS X x86 (64-bit) (February 19, 2009)



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