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Homework Help: Challenging Trig Equation

  1. Feb 15, 2012 #1
    1. The problem statement, all variables and given/known data

    x is [0,2π]
    2. Relevant equations

    3. The attempt at a solution
    Using trig identities:

    Please help me with this problem. I have no idea where to go from here. Thanks.
    Last edited: Feb 15, 2012
  2. jcsd
  3. Feb 15, 2012 #2
    I've further simplified it to:


    Does this make it easier? Please help.
    Last edited: Feb 15, 2012
  4. Feb 16, 2012 #3


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    I was going to give this a try but had to head off to work, but now that I'm looking at it I'm honestly stuck as well...

    This doesn't seem to be making things simpler.

    I got here also and couldn't do much with it.

    I also converted [tex]\sin(2x)+\sqrt{3}\cos(2x)[/tex] into the [tex]R\sin(2x+\theta)[/tex] form and got [tex]2\sin(2x+\frac{\pi}{3})[/tex]

    so what needs to be solved now is


    But I'm kind of stuck here as well.

    We'll get back to you!
  5. Feb 16, 2012 #4


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    When sin(α)=sin(β) either




    Last edited: Feb 16, 2012
  6. Feb 16, 2012 #5
    First, make everything in the angle 2x. This gives (as you already know)


    Now the trick is to use Weierstrass substitution (which is a handy technique in integration but it works here too).

    Let [itex]t=\tan(x)[/itex], then


    this will give a polynomial in t which should be easier to solve.

    Not saying that this is the easiest way, but it gives a solution nonetheless.
  7. Feb 17, 2012 #6
    Thanks guys :)
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