       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:=
FullSimplify[ff]

Out=
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:=
o1=FullSimplify[Together[TrigToExp[ff]]]

Out=
(1/4)*Sqrt[1 + 1/Sqrt]*Pi

or as an another way take

In:=
o2=FullSimplify[TrigFactor //@ ff]

Out=
(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:=
FullSimplify[ff, TransformationFunctions -> {Automatic, TrigToExp,
Together}]

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

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

Thank you very much!

Dimitris

```

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