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Homework Help: Tring inequality

  1. Sep 27, 2010 #1
    1. The problem statement, all variables and given/known data
    solve the following equations or inequalties for x in the interval [0,2pi)

    2cos^2(x) + 1 = 3cos(2x)

    2. Relevant equations



    3. The attempt at a solution

    My attempt at the problem:

    2cosx(cos2x) + 1 = 3cos(2x)
    2cosx(cos^2x - sin^2x) + 1 = 3cos(2x)
    2cos^3x - 2cosxsin^2x + 1 = 3(1-2sin^2x)
    2cos^3x - 2cosxsin^2x + 1 = 3-6sin^2x
    2cos^3x - 2cosxsin^2x + 1 - 3 + 6sin^2x = 0

    and im getting lost here...


    please help,
     
  2. jcsd
  3. Sep 27, 2010 #2
    use this identity:
    Cos(2x) = 2Cos^2(x) - 1
     
  4. Sep 28, 2010 #3

    Mark44

    Staff: Mentor

    You have a mistake in your first step, below. 2cos2(x) is not equal to 2cos(x)*cos(2x). Use the identity that JonF gave to rewrite 3cos(2x) in terms of cos2(x).
     
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