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)