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Math Help - Help in simplifying equasion

  1. #1
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    Help in simplifying equasion

    Hi All,
    I'm new to this blessed site.
    Would appreciate someone's help in simplifying the following equation:



    Many thanks !
    Last edited by naorca; November 6th 2009 at 02:36 AM.
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  2. #2
    Super Member Deadstar's Avatar
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    sec^2(x) = 1+tan^2(x),

    Can ya finish?
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  3. #3
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  4. #4
    Super Member Deadstar's Avatar
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    \frac{\tan(x) \sin(x)}{\sec^2(x) - 1} = \frac{\tan(x) \sin(x)}{1 + \tan^2(x) - 1} = \frac{\tan(x) \sin(x)}{\tan^2(x)} = \frac{\sin(x)}{\tan(x)}.

    And \tan(x) = \frac{\sin(x)}{\cos(x)} so we have...

    \frac{\sin(x)}{\tan(x)} = \frac{\sin(x)}{\frac{\sin(x)}{\cos(x)}} = \cos(x).
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  5. #5
    Super Member Deadstar's Avatar
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    If you need clarification on the last step then...

    \frac{\cos(x)}{\cos(x)} = 1 so...

    \frac{\sin(x)}{\frac{\sin(x)}{\cos(x)}} \cdot 1 = \frac{\sin(x)}{\frac{\sin(x)}{\cos(x)}} \cdot \frac{\cos(x)}{\cos(x)} = \frac{\sin(x)\cos(x)}{\frac{\sin(x)\cos(x)}{\cos(x  )}} = \frac{\sin(x) \cos(x)}{\sin(x)} = \cos(x)
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  6. #6
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    Thanks !
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