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Homework Help: Need help with this trig identity

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data

    (1 + cosθ) / (1 - cosθ) = (1 + secθ) / (secθ - 1)

    2. Relevant equations

    using only the quotient identities, pythagorean identities, and reciprocal identities

    3. The attempt at a solution

    didnt know where to start...
  2. jcsd
  3. Nov 19, 2009 #2


    Staff: Mentor

    Start on the right side.
  4. Nov 19, 2009 #3


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    Homework Helper

    lol Mark44.

    Key word is reciprocal identity, and this should be obvious since [itex]cos\theta[/itex] is the reciprocal of [itex]sec\theta[/itex] and vice versa.
  5. Nov 19, 2009 #4
    kk got it.

    =(1 + secθ) / (secθ - 1)
    =(1 + 1/cosθ) / (1/cosθ - 1)
    =([cosθ+1] / cosθ) / ([1-cosθ] / cosθ)
    =[(cosθ+1)(cosθ)] / [(1-cosθ)(cosθ)]
    cancel cosθ
    =(1 + cosθ) / (1 - cosθ)
  6. Nov 19, 2009 #5
    oh wow, all these question are so easy now, thanks for the advice about the reciprocal.
  7. Nov 19, 2009 #6


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    Homework Helper

    No problem :smile:

    I remember starting off with trig identities... I would have to say that was the hardest and most stressful topic to learn. If you don't have someone like your teacher to help you out with those, you can get lost in a question for hours! Well, at least thats what me and a few of my friends did.

    It all comes to you eventually with much practice on this topic though. Good luck.
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