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HELP trigonometry

  1. Nov 29, 2009 #1
    HELP!!! trigonometry

    1. The problem statement, all variables and given/known data
    without using calculator:
    prove that: sin18 = √5-1/4

    2. Relevant equations
    Double-angle formulae
    sin 2a = 2sin a.cos a
    cos 2a = cos^2a - sin^2a = 1 - 2sin^2a = 2cos^2a - 1
    sin^2 a + cos^2 a=1

    3. The attempt at a solution
    let 18=a
    sin a = sin(90 - a) = cos 4a
    cos 4a = 1 - 2sin^2 2a
    = 1 - 2(2sin a.cos a)^2
    = 1 - 2(4sin^2 a.cos^2 a)
    = 1 - 8sin^2 a.cos^2 a
    = 1 - 8sin^2a(1-sin^2a)
    = 1 - 8sin^2a + 8sin^4a
    i can't go further than that ?????!!
     
  2. jcsd
  3. Nov 29, 2009 #2

    Mentallic

    User Avatar
    Homework Helper

    Re: HELP!!! trigonometry

    So now what you have is:

    [tex]sina=1-8sin^2a+8sin^4a[/tex]

    Hint: To solve this quartic, search for rational factors with the rational factor theorem.
     
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