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Math Help - Find A

  1. #1
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    Find A

    Show that secA+tanA=tan(\frac{\pi}{4}+\frac{A}{2}) and deduce a similar expression for secA-tanA
    Hence find the surd form of the values of tan\frac{7\pi}{12} and tan\frac{\pi}{12}
    i have completed the first two parts, for the second i got the equality tan(\frac{\pi}{4}-\frac{A}{2})
    now i only have the last part to do and i'm lost.
    Last edited by arze; July 12th 2009 at 10:28 PM.
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  2. #2
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    I am not completely sure about using \tan(\frac{\pi}{4}-\frac{A}{2}) to get to the surd value for tan\frac{7\pi}{12} and tan\frac{\pi}{12}, however I do know another way:

    You can try represent \frac{7\pi}{12} and \frac{1\pi}{12} with angles that we now the surd form:
    \frac{7\pi}{12} = \frac{4\pi}{12} + \frac{3\pi}{12}
    \frac{7\pi}{12} = \frac{4\pi}{12} - \frac{3\pi}{12}
    By using a double angle formula, you can now find the exact value of tan\frac{7\pi}{12} and tan\frac{\pi}{12}.
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  3. #3
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    Quote Originally Posted by arze View Post
    Show that secA+tanA=tan(\frac{\pi}{4}+\frac{A}{2}) and deduce a similar expression for secA-tanA
    Hence find the surd form of the values of tan\frac{7\pi}{12} and tan\frac{\pi}{12}
    i have completed the first two parts, for the second i got the equality tan(\frac{\pi}{4}-\frac{A}{2})
    now i only have the last part to do and i'm lost.
    You require \frac{\pi}{4} + \frac{A}{2} = \frac{7 \pi}{12} \Rightarrow A = \frac{2 \pi}{3}. So substitute A = \frac{2 \pi}{3} into the first expression.

    Similarly, substitute A = \frac{\pi}{3} into the second expression.
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