Expansion for large tan(x)

  • Thread starter physlad
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  • #1
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Main Question or Discussion Point

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:

Answers and Replies

  • #2
798
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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.
 
  • #3
21
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Thank you very much, JJacquelin! now I see it :D
 

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