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Homework Help: Solve cos2xsinx=1

  1. Mar 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Simplify AND Solve for X
    cos2xsinx=1


    2. Relevant equations
    The triples, doubles


    3. The attempt at a solution
    cos2xsinx=1
    (cos^2x-sin^2x)(sinx)=1
    (-1x)(sinx)=1
    -sinx=1
    sinx= -1
    ?


    ..

    :-/

    Help.. :)
     
  2. jcsd
  3. Mar 30, 2010 #2

    Dick

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    Re: Cos2xsinx=1

    The maximum absolute value of cos(2x) and sin(x) is 1. So the only way you can solve that is if cos(2x)=1 AND sin(x)=1 or cos(2x)=(-1) AND sin(x)=(-1). Is either of those possible? If so which one?
     
  4. Mar 31, 2010 #3
    Re: Cos2xsinx=1

    I have no idea may i have another clue
     
  5. Mar 31, 2010 #4
    Re: Cos2xsinx=1

    anyone?
     
  6. Mar 31, 2010 #5

    Dick

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    Re: Cos2xsinx=1

    Graph cos(2x) and sin(x) on [0,2pi]. Or do this cos^2(x)-sin^2(x)=1-2*sin^2(x). So you have (1-2*sin^2(x))*sin(x)=1. If sin(x)=u then you have (1-2*u^2)*u=1. That's a cubic equation for u. Can you find the real root?
     
    Last edited: Mar 31, 2010
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