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Math Help - cosec(cos^-1 (1/y)

  1. #1
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    cosec(cos^-1 (1/y)

    Can someone please check this for me thanks.

    Question is \cos ec(\cos ^{ - 1} (\frac{1}{y})) =


    This is what I worked it to be
    <br />
\begin{array}{l}<br />
 {\rm let }\theta  = \cos ^{ - 1} (\frac{1}{y}) \\ <br />
 \cos \theta  = \frac{1}{y} \\ <br />
 \cos ^2 \theta  + \sin ^2 \theta  = 1 \\ <br />
 (\frac{1}{y})^2  + \sin ^2 \theta  = 1 \\ <br />
 \sin ^2 \theta  = 1 - (\frac{1}{y})^2  \\ <br />
 \sin \theta  = \sqrt {1 - \left( {\frac{1}{y}} \right)^2 }  \\ <br />
 \cos ec\theta  = \frac{1}{{\sin \theta }} = \frac{1}{{\sqrt {1 - \left( {\frac{1}{y}} \right)^2 } }} \\ <br />
 \end{array}<br />

    Is it right?
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  2. #2
    Super Member Showcase_22's Avatar
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    I did it a similar way and got what you did in a different form:



    My working was virtually the same.
    Last edited by Showcase_22; September 11th 2008 at 05:33 AM. Reason: a typo, yet again.
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  3. #3
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    not sure how to get from what I go to what you have ie y/(y+1)(y-1)
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  4. #4
    Super Member Showcase_22's Avatar
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