Trig Equation

  • Thread starter DERRAN
  • Start date
  • #1
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Homework Statement


Solve the Equation:

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

Homework Equations





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.
 

Answers and Replies

  • #2
Cyosis
Homework Helper
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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:
  • #3
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[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.
 
  • #4
34
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thanks
 

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