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Math Help - Trig Identity

  1. #1
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    Trig Identity

    Tried all I could on this one. I think I'm making it out to be harder than it's supposed to be...

    (sec(x))/(sec(x)-tan(x))=sec^2(x)+sec(x)tan(x)

    Any help would be greatly appreciated.
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  2. #2
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    Hey, try expressing sec(x) and tan(x) in terms of sines and cosines first, cancel what you can.

    You should get  \frac{1}{1 - \sin (x)}

    The trick here is to multiply the numerator and denominator by  1 + \sin (x)

    Then use the identity  \sin^2 x + \cos^2 x = 1 on the denominator.

    Convert back to sec and tan and that should be it.
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  3. #3
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    \sec^2{x} + \sec{x}\tan{x} = \sec{x}(\sec{x} + \tan{x})

     = \frac{\sec{x}(\sec{x} + \tan{x})(\sec{x} - \tan{x})}{\sec{x} - \tan{x}}

     = \frac{\sec{x}(\sec^2{x} -\tan^2{x}) }{\sec{x} - \tan{x}}

     = \frac{\sec{x}(1)}{\sec{x} - \tan{x}}

     = \frac{\sec{x}}{\sec{x} - \tan{x}}.
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  4. #4
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    Thanks a lot guys. Your help was a godsend.
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