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# pure 5 ---Complex number HELP!!!!!!!!!!!!!!!!!!!! watch

1. Express the following in the terms of multiple angles.
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2. Have you tried expressing both sin^3 and cos^4 in terms of multiples of sin x and cos x, sin 2x, cos 2x, etc... respectively?
3. If you change everything to powers of cos first, then you can use De Moivre to express these as cosines of multiples of theta, and add the results together.

I don't know if it will work by using both sin and cos, as you'd end up with terms in sin3x.cos4x, I think, which isn't as neat.

My solution's pretty lengthy - I don't know if they'd set this question in an exam (as you say P5, not P6, I assume you're not doing the Edexcel syllabus), as it's fairly repetetive. There might be a faster way, though.
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4. (Original post by Werther)
If you change everything to powers of cos first, then you can use De Moivre to express these as cosines of multiples of theta, and add the results together.

I don't know if it will work by using both sin and cos, as you'd end up with terms in sin3x.cos4x, I think, which isn't as neat.

My solution's pretty lengthy - I don't know if they'd set this question in an exam (as you say P5, not P6, I assume you're not doing the Edexcel syllabus), as it's fairly repetetive. There might be a faster way, though.
Thank you very much.

ps: I am doing OCR MEI.

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Updated: March 20, 2004
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