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Homework Help: Prove trigonometric expression

  1. Dec 7, 2011 #1

    sharks

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    Gold Member

    1. The problem statement, all variables and given/known data
    Prove that sec^(2)(x/2) divided by 1 - tan^(2)(x/2) is sec x


    2. Relevant equations
    Trig identities.


    3. The attempt at a solution
    I used the identity: 1 + tan^2(x) = sec^2(x)

    I get for numerator: 1 + tan^2(x/2)
    I kept denominator same: 1 - tan^2(x/2)
    I get the impression (intuition?) that this can be solved in its current form. But then since i couldn't after a while, i just went on to expand tan^2(x/2) using the double angle formula to get expressions in terms of tan(x). It turned into something lengthy, so i doubt that i'm doing it right.
     
  2. jcsd
  3. Dec 7, 2011 #2

    Mentallic

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    Homework Helper

    You're headed in the wrong direction. Notice that

    [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}[/tex]

    and

    [tex]\sec(x)=\frac{1}{\cos(x)}[/tex]

    so convert these and simplify, then you can easily apply a double angle formula.
     
  4. Dec 7, 2011 #3

    sharks

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    Gold Member

    OK, got it. Thanks, Mentallic.
     
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