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MathGroup Archive 2007

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simplification

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77365] simplification
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Thu, 7 Jun 2007 03:55:39 -0400 (EDT)

Hello.

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]];

Let's make an attempt to simplify ff.

In[190]:=
FullSimplify[ff]

Out[190]=
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]]

Let's try harder

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]

My first question is how someone can arrive from o1 to o2 and vice
versa.

Secondly,

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?

Thirdly, why the following does suceed?

In[3]:=
FullSimplify[ff, TransformationFunctions -> {Automatic, FullSimplify}]

Out[3]=
(1/8)*Pi*Csc[Pi/8]

Thank you very much!

Dimitris



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