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Math Help - Prove given identities

  1. #1
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    Prove given identities

    SecA TanA
    ----- - ----- = 1
    CosA Cot A

    Please help, I don't know where to start or how to complete this.
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  2. #2
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    Re: Prove given identities

    Rewrite everything in terms of sine and cosine.
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  3. #3
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    Re: Prove given identities

    Think of the pythagorean identity tan^2(x) + 1 = sec^2(x)

    See how it can be re-arranged to look like sec^2(x) - tan^2(x) = 1

    Now, how are \frac{sec(x)}{cos(x)} and sec^2(x) related?

    How are \frac{tan(x)}{cot(x)} and tan^2(x) related?
    Last edited by amillionwinters; November 9th 2012 at 05:10 PM.
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  4. #4
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    Re: Prove given identities

    Hello, hachm361!

    \text{Prove: }\:\frac{\sec A}{\cos A} - \frac{\tan A}{\cot A} \:=\:1

    Do you know any basic identities . . . like these?

    . . \cos A \,=\,\frac{1}{\sec A} \qquad \cot A \,=\,\frac{1}{\tan A} \qquad \sec^2\!A - \tan^2\!A \:=\:1

    If you don't, you need more help than we can offer.


    We have: . \frac{\sec A}{\cos A} - \frac{\tan A}{\cot A} \;=\;\frac{\sec A}{\frac{1}{\sec A}} - \frac{\tan A}{\frac{1}{\tan A}} \;=\;\sec^2\!A - \tan^2\!A \;=\;1
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