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Math Help - Trigonomertric identities

  1. #1
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    Question Trigonomertric identities

    [tex]cos20°cos100°+cos100°cos140°-cos140°cos200°=\frac{-3}{4}[tex]
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by matsci0000 View Post
    [tex]cos20°cos100°+cos100°cos140°-cos140°cos200°=\frac{-3}{4}[tex]
    cos20°cos100°+cos100°cos140°-cos140°cos200°

    = cos20°cos100°+cos100°cos140°+cos140°cos20°

    Now, see <br />
sec\frac{\pi}{9},sec\frac{5\pi}{9},sec\frac{7\pi}{  9}<br />
are the roots of equation

    <br />
sec^{3}\theta+6sec^{2}\theta-8=0<br />

    see thread: http://www.mathhelpforum.com/math-he...trigo-sum.html

    hence, sec\frac{\pi}{9}*sec\frac{5\pi}{9}*sec\frac{7\pi}{  9}=8

    = cos20°cos100°+cos100°cos140°+cos140°cos20°

    = sec\frac{\pi}{9}*sec\frac{5\pi}{9}*sec\frac{7\pi}{  9} \left(<br />
 sec\frac{\pi}{9}+sec\frac{5\pi}{9}+sec\frac{7\pi}{  9} \right)<br />

    = \frac{-6}{8}

    = \frac{-3}{4}
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