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    Require assistance with a question from one of TeeEm's IYGB Special Papers:

    4cos(x)cos(2x)cos(5x)+1=0.

    First I tried using the Prosthaphaeresis Formulae to get cos(2x)+cos(4x)+cos(6x)+cos(8x)+ 1=0, but that didn't seem to be any more solvable. Then I wrote it as a polynomial in cos(x): it ended up being a quartic in cos^2x that does factorise according to WolframAlpha, but gives surds as answers that are then impossible to turn into the required values of x without a calculator. Thus any assistance would be appreciated.
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    Have another look at cos(2x)+cos(4x)+cos(6x)+cos(8x)+ 1=0. Does it remind you of anything?
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    Maybe double angle formulae: cos(2x)+2cos^2(2x)-1+cos(6x)+4cos^2(2x)-2+1=0?
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    (Original post by constellarknight)
    Maybe double angle formulae: cos(2x)+2cos^2(2x)-1+cos(6x)+4cos^2(2x)-2+1=0?
    This question is from the IYGB, Special paper B and it requires tricks and manipulations
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    I know it is, I was doing the paper and got stuck on it. So since the solution isn't on your website yet, care to give me a hint about the "tricks and manipulations" required?
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    (Original post by constellarknight)
    I know it is, I was doing the paper and got stuck on it. So since the solution isn't on your website yet, care to give me a hint about the "tricks and manipulations" required?
    I'd guess he's looking for a complex approach. Are you familiar with De Moivre's theorem and that kind of stuff?
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    Yes, but I don't see how it could be applied as there are no imaginary terms.
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    (Original post by constellarknight)
    Yes, but I don't see how it could be applied as there are no imaginary terms.
    BTW, you ought to reply to my post, else I won't see any response till I look at the thread.

    You have to create the imaginary terms yourself, in a useful sort of way. Start by considering a sum of complex exponentials that look like what you already have. Then consider real and imaginary parts.
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    Well, the LHS is 1+Re(cis(2x)+cis(4x)+cis(6x)+cis (8x))... I really have no idea here...
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    (Original post by constellarknight)
    I know it is, I was doing the paper and got stuck on it. So since the solution isn't on your website yet, care to give me a hint about the "tricks and manipulations" required?
    it does not require complex numbers.
    here it is
    Attached Images
  1. File Type: pdf trig.pdf (269.5 KB, 66 views)
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    Thanks for the solution. But how did you think to multiply by sin x in the first place? Was it just "intuition" or is this a general method for equations with a product of sin or cos terms?
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    (Original post by TeeEm)
    it does not require complex numbers.
    here it is
    Brilliant!
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    (Original post by Zacken)
    Brilliant!
    did you like it ...?
    an evil question ... which reminds me I need to write solutions to this paper.
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    (Original post by TeeEm)
    did you like it ...?
    an evil question ... which reminds me I need to write solutions to this paper.
    Very much so!

    Kind of wished I'd given it a try before opening your solutions, eurgh.
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    Yes, you've been rather slow with IYGB stuff recently: indeed, after the question paper was attached to the forum thread, it wasn't put on your own website for about a week.
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    (Original post by constellarknight)
    Yes, you've been rather slow with IYGB stuff recently: indeed, after the question paper was attached to the forum thread, it wasn't put on your own website for about a week.
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    What is that image supposed to be of?
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    Just out of interest, roughly what level of question is this? I'm studying A level maths independently, with a view to sitting all 6 exams (C1-4, S1, D1) this year. I'm a little behind schedule, just about to get going on C3/4 for the first time, but was still fairly confident I've got enough time (especially after recently discovering examsolutions.net). I'm hoping this question is way above C3/4 level, as if not I'm pretty sure I'm in more trouble than I may have realised...
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    It is indeed above ordinary C3/C4 level: the IYGB SP papers are for exceptional people. Hence why despite me having got an A* in A-Level Maths when I was 10 and being a member of MENSA, I still couldn't do this question - although obviously I have been able to do most of the other ones from IYGB SPs.
 
 
 
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