Use de Moivre's formula and the Binomial theorem to derive a formula that expresses cos5x as a polynomial in cosx, or more precisely determine the constants ABC.

This is what I have done.. is it correct or im I totally wrong?

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- Dec 22nd 2009, 04:15 AMsf1903De Moivre's formula and Binomial theorem
Use de Moivre's formula and the Binomial theorem to derive a formula that expresses cos5x as a polynomial in cosx, or more precisely determine the constants ABC.

This is what I have done.. is it correct or im I totally wrong?

Attachment 14537 - Dec 22nd 2009, 04:39 AMI-Think
The question says to use De' Moivre's Theorem and I didn't see you use it (I could be wrong), so I'll start it.

Expanding

Now compare terms with real coefficients, these terms are those that will make - Dec 22nd 2009, 05:30 AMsf1903
- Dec 22nd 2009, 11:55 AMSoroban
Hello, sf1903!

Quote:

Use de Moivre's formula and the Binomial theorem to derive a formula

that expresses as a polynomial in

DeMoivre's formula says: . .[1]

Expand the right side:

. .

. . . .

. . . .

Equate real and imaginary components:

. . . .

. . . .

. . . .

. . . .