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Trig Equation

  1. Jun 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve the Equation:

    sec2A - 3tanA - 5=0, for A [tex]\in[/tex][-90,0]

    2. Relevant equations



    3. The attempt at a solution
    [tex]\frac{1}{cos^{2}A}[/tex] - [tex]\frac{3sinA}{cosA}[/tex] -5 =0

    [tex]\frac{1-3sinA.cosA}{cos^{2}A}[/tex] -5 = 0

    ???
    Did I go wrong? If not i'm stuck. Please help. Thank you.
     
  2. jcsd
  3. Jun 16, 2009 #2

    Cyosis

    User Avatar
    Homework Helper

    You didn't go wrong, but the form you wrote it in only makes it harder. I suggest you write the [itex]\sec^2 A[/itex] term in terms of the tangent. Do you know how?
     
    Last edited: Jun 16, 2009
  4. Jun 16, 2009 #3
    [tex]sec^2A=\frac{1}{cos^2A}=\frac{sin^2A+cos^2A}{cos^2A}=\frac{sin^2A}{cos^2A}+\frac{cos^2A}{cos^2A}=tan^2A+1[/tex]

    Just substitute and solve the quadratic equation.

    Regards.
     
  5. Jun 16, 2009 #4
    thanks
     
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