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Proving Identity

  1. Nov 7, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that [tex]\prod_{k=1}^{n-1}\sin\frac{k\pi}{2n}=\frac{\sqrt{n}}{2^{n-1}}[/tex]

    3. The attempt at a solution

    I have no idea where to start.
  2. jcsd
  3. Nov 7, 2007 #2


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    Let [itex]\zeta[/itex] be the primitive (2n)th root of unity, i.e. [itex]\zeta = \exp(\pi i / n)[/itex]. Try to simplify [itex]|1 - \zeta^k|[/itex] (where k is some positive integer). Then try playing around with x^(2n) - 1.
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