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Trigonometric Functions And Identities

  1. Jun 1, 2008 #1
    Hi there,

    I am struggling to solve for x in the following problem:-

    Find all values of x in the interval 0<= x <= 360 for which: tan^2(x) = 5sec(x) - 2

    I have used the identity tan^2(x) + 1 = sec^2(x) to get:

    sec^2(x) - 1 = 5sec(x) - 2

    and rearranged to get

    sec^2(x) - 5sec(x) + 1 = 0

    but I cant factor this or solve for x. Can anyone help please?
  2. jcsd
  3. Jun 1, 2008 #2


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    Why did you spend all of that effort to turn it into a quadratic equation?
  4. Jun 1, 2008 #3
    I assumed that I need to get all the trig functions of the same type before I can solve for x. Using the identity for sec^2(x) seemed the obvious choice...which lead me to a quadratic. I couldn't see how else to solve for x. I also tried converting everything in terms of cos (x) which was more messy. I may be mistaken, but from previous questions I have answered like this, tend to lead to a quadratic to factor for a solution/s for x.
  5. Jun 1, 2008 #4


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    Is factoring the only method you know for solving quadratic equations, or do you know other methods?
  6. Jun 1, 2008 #5
    Completing the square, or using the quadratic formula are another two methods.
  7. Jun 1, 2008 #6
    Thanks, tried completing the square to solve the quadratic and this worked.
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