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Math Help - Prove

  1. #1
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    Question Prove

    Prove

    (Secθ-tanθ)/(Secθ+tanθ) = 1- 2 Secθ X tanθ + 2 tanēθ
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  2. #2
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    Hello prantik007
    Quote Originally Posted by prantik007 View Post
    Prove

    (Secθ-tanθ)/(Secθ+tanθ) = 1- 2 Secθ X tanθ + 2 tanēθ
    Using the identities:
    \sec^2\theta -\tan^2\theta =1
    and
    (a+b)(a-b)=a^2-b^2
    multiplying top-and-bottom by \sec\theta -\tan\theta, we get:
    \frac{\sec\theta -\tan\theta}{\sec\theta +\tan\theta}=\frac{(\sec\theta -\tan\theta)^2}{\sec^2\theta -\tan^2\theta}
    =\sec^2\theta -2\sec\theta\tan\theta+\tan^2\theta

    =1+\tan^2\theta -2\sec\theta\tan\theta+\tan^2\theta

    =1 -2\sec\theta\tan\theta+2\tan^2\theta
    Grandad
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  3. #3
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    Last edited by prantik007; March 9th 2010 at 10:01 AM.
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