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# FP2 Complex Numbers watch

1. Express cos(^5) θ in terms of cosines of multiples of θ.
What is the method for doing this?
2. De Moivre's theorem?

(Admittedly I haven't really done the working for this yet )
3. Express Cos theta in terms of e, put all that to the power of 5 and use the binomial theorem to expand, then at the end just manipulate it to convert it back to trigonometric terms.
4. (Original post by You Failed)
Express Cos theta in terms of e, put all that to the power of 5 and use the binomial theorem to expand, then at the end just manipulate it to convert it back to trigonometric terms.

I agree this is how you start; it gives cos(5theta) in terms of powers of cos(theta). But in answering this question there will be other powers of cos left - which must be disposed of by expanding things like cos(3theta)
5. (Original post by ian.slater)
I agree this is how you start; it gives cos(5theta) in terms of powers of cos(theta). But in answering this question there will be other powers of cos left - which must be disposed of by expanding things like cos(3theta)
Yeah there will be other powers but like you said, you just expand them and use identities to get rid of them.

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