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MathGroup Archive 2007

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questions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77513] questions
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Mon, 11 Jun 2007 04:24:24 -0400 (EDT)

Hello.

This appeared recently, but sice there was
no response, I make one more attempt.

ff = Pi*Cos[1/7*Pi]*Cos[2/7*Pi]*
  Cos[3/7*Pi]/Sin[Pi*Cos[1/7*Pi]*Cos[2/7*Pi]*Cos[3/7*Pi]];

I try to simplify ff.

In[194]:=
o1=FullSimplify[Together[TrigToExp[ff]]]
Out[194]=
(1/4)*Sqrt[1 + 1/Sqrt[2]]*Pi

or as an another way take

In[199]:=
o2=FullSimplify[TrigFactor //@ ff]
Out[199]=
(1/8)*Pi*Csc[Pi/8]

o1 was obtained by FullSimplify[Together[TrigToExp[ff]]].

Why doesn't

In[206]:=
FullSimplify[ff, TransformationFunctions -> {Automatic, TrigToExp,
Together}]

Out[206]=
Pi*Cos[Pi/7]*Cos[(2*Pi)/7]*Cos[(3*Pi)/7]*Csc[Pi*Cos[Pi/7]*Cos[(2*Pi)/
7]*Cos[(3*Pi)/7]]

do the same thing? What I miss here?

Also, why the following does suceed?

In[213]:=
FullSimplify[ff, TransformationFunctions -> {Automatic,
FullSimplify}]
Out[213]=
(1/8)*Pi*Csc[Pi/8]

Thank you very much!



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