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Math Help - Trig. Identities?

  1. #1
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    Trig. Identities?

    [not sure if this would come under trig identities, (part B of this question is differentiation, but i'm not needing help with that)]



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  2. #2
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    \frac{\sin^3(x)+\cos^2(x)}{\sin^2(x)}

    \frac{\sin^3(x)+(1-\sin^2(x))}{\sin^2(x)}

    \sin(x)+\sin^{-2}(x)-1
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  3. #3
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    EDIT: How do you get -1?
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  4. #4
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    you have the identity that:

    \sin^2(x)+\cos^2(x)=1

    so then \cos^2(x)=1-\sin^2(x)

    so we then have:

    <br />
\frac{\sin^3(x)}{\sin^2(x)}+\frac{1}{\sin^2(x)}{\c  olor{blue} -\frac{\sin^2(x)}{\sin^2(x)}}

    so:

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