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Help! solving by using trig identity

  1. Dec 16, 2008 #1
    1. The problem statement, all variables and given/known data

    sinx cos2x=1

    x is greater than or equal to 0 and less than 2pi

    2. Relevant equations

    What I used:
    1-2sin2x
    cos2x-sin2x

    but there might be one that I didn't and should have...

    3. The attempt at a solution

    Basically I have substituted to the point that I can, I feel pretty bad since this is a review..

    sinx cos2x=1

    sinx (1-2sin2x)=1

    basically didn't know where to go from there..

    and

    sin cosx=1
    sinx (cos2x-sin2x)=1
    sinx(cos2x)-sin3x=1
    sinx(1-sin2x)-sin3x=1

    sinx-sin3x-sin3x=1

    And that one stopped there...
    we are supposed to only use trigonometric identities, nothing more nothing less; and once again I don't understand how I can not get this since it is a review..

    Thanks
     
  2. jcsd
  3. Dec 16, 2008 #2

    Mentallic

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    Homework Helper

    Yes can you see how this is a cubic function in sinx?
    Maybe if you rearranged it, it will become more clear.
     
  4. Dec 18, 2008 #3
    sinx (1-sin2x)=1

    try multiplying out the brackets and rearranging the equation so that its =0 from there you should get a quadratic equation.
     
  5. Dec 18, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, you get a cubic equation as Mentallic said. Fortunately one that is easy to solve.
     
  6. Dec 18, 2008 #5
    Haha, wow surprised I didn't see that one, thanks guys!
     
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