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Math Help - Please find exact value

  1. #1
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    Please find exact value

    Please find exact value
    <br />
tan \frac{19\pi}{12}

    The correct answer is -2-{\sqrt 3}

    tan \frac{19\pi}{12}

    -tan 75=-tan (45 +30)=- \frac{3+\sqrt 3}{3-\sqrt 3}

    What am I doing wrong?

    Thank you
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  2. #2
    Senior Member DivideBy0's Avatar
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    Melbourne, Australia
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    Quote Originally Posted by oceanmd View Post
    Please find exact value
    <br />
tan \frac{19\pi}{12}

    The correct answer is -2-{\sqrt 3}

    tan \frac{19\pi}{12}

    -tan 75=-tan (45 +30)=- \frac{3+\sqrt 3}{3-\sqrt 3}

    What am I doing wrong?

    Thank you
    You are correct, you just need to rationalize the denominator:

    -\frac{3+\sqrt{3}}{3-\sqrt{3}}=-\frac{3+\sqrt{3}}{3-\sqrt{3}}\left(\frac{3+\sqrt{3}}{3+\sqrt{3}}\right  )=-\frac{12+6\sqrt{3}}{6}=-(2+\sqrt{3})=-2-\sqrt{3}
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  3. #3
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    Thank you
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