Re: Simplification question
- To: mathgroup at smc.vnet.net
- Subject: [mg110396] Re: Simplification question
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Wed, 16 Jun 2010 05:40:22 -0400 (EDT)
$Version
7.0 for Mac OS X x86 (64-bit) (February 19, 2009)
eqn = 1/2 Log[(Exp[a + b] + Exp[-a - b])/
(Exp[-a + b] + Exp[a - b])] ==
ArcTanh[Tanh[a] Tanh[b]];
eqn // TrigToExp //
Simplify[#, Element[{a, b}, Reals]] &
True
eqn // TrigToExp // Simplify //
PowerExpand
True
Bob Hanlon
---- Yaroslav Bulatov <yaroslavvb at gmail.com> 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?