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Expansion for large tan(x)

  1. Oct 30, 2011 #1
    Hi, I was reading a review and I saw this equation,

    [tex]A^2 = \frac{|B^2 - C^2|}{\sqrt{(1-sin^2(2x))}} - C^2 - B^2 - 2D^2[/tex]

    Then at some point he writes: "expanding for large [itex]tan(x)[/itex], this expression becomes,

    [tex]A^2 = -2(C^2 + D^2) + \frac{2}{tan^2(x)}(B^2 - C^2) + O(1/tan^4(x)) [/tex]

    Could anybody explain how did this happen?
    Last edited: Oct 30, 2011
  2. jcsd
  3. Oct 31, 2011 #2
    Let t = 1/tan(x)
    Compute sin(2x) as a function of t.
    Bring it back into the equation.
    Develop it as a a series for t.
    When tan(x) tends to infinity t tends to 0.
    Remplace t by 1/tan(x) in the series.
    You will obtain the expected result.
  4. Oct 31, 2011 #3
    Thank you very much, JJacquelin! now I see it :D
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