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Math Help - Sum and Difference Formulas

  1. #1
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    Sum and Difference Formulas

    Hello again.
    I'm asked to find the exact value of tan 15deg.
    To make it short, I got (3 - sqrt(3)) / (3 + sqrt(3)),
    but in the back of the book, they got 2 - sqrt(2).
    How am I suppose to get that from what I got?
    Thanks.
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  2. #2
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
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    Melbourne, Australia
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    \tan{(60-45)} = \frac{\tan{60}-\tan{45}}{1+\tan{60}\tan{45}} = \frac{\sqrt{3}-1}{1+(\sqrt{3})(1)}=\frac{\sqrt{3}-1}{\sqrt{3}+1}

    From here it's just rationalizing the denominator:

    =\frac{(\sqrt{3}-1)(\sqrt{3}-1)}{(\sqrt{3}+1)(\sqrt{3}-1)}=\frac{4-2\sqrt{3}}{3-1}=\frac{4-2\sqrt{3}}{2}=2-\sqrt{3}
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