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Math Help - simplifying the expression

  1. #1
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    simplifying the expression

    I'm having trouble with this

    (1-sin^2(x)) / sin(x) - csc(x)
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by yeunju View Post
    I'm having trouble with this

    (1-sin^2(x)) / sin(x) - csc(x)
    \frac{1-\sin^2x}{\sin x}-\csc x=\frac{1}{\sin x}-\frac{\sin^2x}{\sin x}-\csc x=\dots

    Can you continue?
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  3. #3
    MHF Contributor red_dog's Avatar
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    \frac{1-\sin^2x}{\sin x-\csc x}=\frac{1-\sin^2x}{\sin x-\frac{1}{\sin x}}=\frac{1-\sin^2x}{\frac{\sin^2x-1}{\sin x}}=-\sin x
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by yeunju View Post
    I'm having trouble with this

    (1-sin^2(x)) / sin(x) - csc(x)
    \color{red} sin^2(x) + cos^2(x) = 1 \qquad \implies sin^2(x) - 1 = -cos^2(x)

    If this is your question

    \frac{(1-sin^2(x))}{sin(x)} - csc(x)


    \frac{(1-sin^2(x))}{sin(x)} -\frac{1}{sin(x)}

    \frac{(1-sin^2(x))-1}{sin(x)}

    \frac{-sin^2(x)}{sin(x)}

    -sin(x)
    ------------------------------------------------------------------------
    If your question is

    \frac{1-sin^2(x)}{sin(x) - csc(x)}




    Denominator = sin(x) - csc(x) = sin(x) - \frac{1}{sin(x)}

    <br />
= \frac{sin^2(x) - 1}{sin(x)}

    <br />
= \frac{-cos^2(x)}{sin(x)}


    Numerator = 1-sin^2(x) = cos^2(x)

    So fraction is

    =\frac{cos^2(x)}{\frac{-cos^2(x)}{sin(x)}}

    =\frac{sin(x)}{-1}

    =~ -sin(x)
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