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*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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