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B Factoring quadratic equation (with trig identities used)

  1. Sep 26, 2016 #1
    Is it possible to factor a quadratic equation along the lines of asin^2x -bsin2x+c ? If so, how? The sin2x seems to be a problem since when expanded it becomes 2sinxcosx, but I'm wondering if it is possible, and how it would be done?

    Thanks in advance.
     
  2. jcsd
  3. Sep 26, 2016 #2

    Mark44

    Staff: Mentor

    I don't see any way of doing it. What's the context of this problem? Could there be a mistake leading up to what you show?

    BTW, what you show isn't an equation -- there's no =.
     
  4. Sep 26, 2016 #3

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    a sin2(x) - b sin(2x) + c = 0 (I guess that is what you meant) can be written as ##a \sin^2(x) + c = 2 b \sin(x) \sqrt{1-\sin^2(x)}##, after squaring both sides you get a quadratic equation in sin2(x).
     
  5. Sep 26, 2016 #4

    pasmith

    User Avatar
    Homework Helper

    Is the object to solve [itex]a \sin^2x - b \sin 2x + c = 0[/itex] for [itex]x[/itex]? If so, use the identities [tex]
    \cos^2 x + \sin ^2 x = 1 \\
    \cos^2 x - \sin^2 x = \cos 2x
    [/tex] to express [itex]\sin^2 x[/itex] in terms of [itex]\cos 2x[/itex]; then you'll have something of the form [itex]p \cos 2x - b \sin 2x + q = 0[/itex] which I hope you know how to solve.
     
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