simplifying an ugly expression

• To: mathgroup at smc.vnet.net
• Subject: [mg21958] simplifying an ugly expression
• From: "Mark Leeds" <m.leeds at gte.net>
• Date: Sat, 5 Feb 2000 22:22:25 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```I am a mathematica novice so I don't even know if the
following is a stupid question.

I have the expression shown below :

duck = 1/2(B1*a^2 + B2*ac + B3*c^2 + B4*a + B5*c + B6)

where

B1 = 10 - 6*cos(x) + 3*cos(3x) - 10*cos(4x) + 3*cos(5x)
B2 = 6 - 6*cos(3x) - 6*cos(4x) + 6*cos(5x)
B3= 14  - 5*cos(x) - 2*cos(2x) - 14*cos(3x) + 4*cos(4x) + 3*cos(5x)
B4 = -32 + 32*cos(x) - 16*cos(3x) + 32*cos(4x) - 16*cos(5x)
B5 = -16 + 16*cos(3x) + 16*cos(4x) - 16*cos(5x)
B6 = 32  - 32*cos(x) + 16*cos(3x) - 32*cos(4x) + 16*cos(5x)

I was wondering if there was any way to ask mathematica
to find some expression, temp, which involves a and c
( for example it might be a/(a+c)) and use it
to simplify the expression, duck, so that duck
can be written in the following form called simpduck:

simpduck = f1(temp)*cos(x) + f2(temp)*cos(2x) + f3(temp)*cos(3x)
+ f4(temp)*cos(4x) +f5(temp)*cos(5x).

it is fine if f1=f2=f3=f4=f5 etc and if trigonometric identities
have to
be used so that it only goes upto say cos(3x), this is fine also.

for example, if temp=a/(a+c), then maybe f(temp)=temp^2 or whatever
?

basically, my goal is to have a and c together instead of
seperated.

thank you very much and i apologize if this is impossible to do ?

Mark

```

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