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Math Help - Simplifying

  1. #1
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    Simplifying

    I'm having difficulties simplifying the expression.

     <br />
cos(\frac{pi}2-x)csc(-x)<br />
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  2. #2
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    Quote Originally Posted by Altair_xI View Post
    I'm having difficulties simplifying the expression.

     <br />
cos(\frac{pi}2-x)csc(-x)<br />
    Remember that  \cos \bigg(\frac{\pi}{2} - \theta\bigg) = \sin(\theta)

    And  \csc(\theta) = \frac{1}{\sin(\theta)}

    Hence:

      \cos \bigg(\frac{\pi}{2} - x \bigg) \csc(-x) = \sin(x) \frac{1}{\sin(-x)} = \sin(x) \frac{1}{-\sin(x)} = \frac{\sin(x)}{-\sin(x)} = -1
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  3. #3
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    Quote Originally Posted by Altair_xI View Post
    I'm having difficulties simplifying the expression.

     <br />
cos(\frac{pi}2-x)csc(-x)<br />
    Note that \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b) and

    csc(x) =\frac{1}{\sin(x)} and that

    \sin(-x)=-\sin(x) sine is an odd function

    \cos\left( \frac{\pi}{2}-x\right)\csc(-x)=\frac{\cos\left( \frac{\pi}{2}-x\right)}{\sin(-x)}=

    \frac{\cos(\frac{\pi}{2})\cos(x)+\sin(\frac{\pi}{2  })\sin(x) }{-\sin(x)}= \frac{\sin(x)}{-\sin(x)}=-1
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  4. #4
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    Thank you. I see where I've messed up now. Many thanks.
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