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Math Help - Double/half angle formula

  1. #1
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    Double/half angle formula

    Stuck with this one.
    I am thinking half angle formulae but cant get started
    Im asked to use the top identity to solve the bottom problem
    Thnks in advance

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  2. #2
    Senior Member Stroodle's Avatar
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    I think the formula is:

    tan(2\theta)=\frac{2tan(\theta)}{1-tan^2(\theta)}

    So,

    tan(\frac{\pi}{4})=\frac{2tan(\frac{\pi}{8})}{1-tan^2(\frac{\pi}{8})}
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  3. #3
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    Thanks
    How would I work out the values?
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  4. #4
    Senior Member Stroodle's Avatar
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    Hmm, are you sure you wrote the rest of the question correctly?

    sin(\frac{\pi}{8})=\frac{\sqrt{2-\sqrt{2}}}{2}

    and,

    cos(\frac{\pi}{8})=\frac{\sqrt{2+\sqrt{2}}}{2}

    so,

    tan(\frac{\pi}{8})=\frac{\frac{\sqrt{2-\sqrt{2}}}{2}}{\frac{\sqrt{2+\sqrt{2}}}{2}}=\sqrt{  3-2\sqrt{2}}
    Last edited by Stroodle; April 8th 2010 at 07:49 PM. Reason: added info
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