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Math Help - Integral of cos^2(x)/sinx

  1. #1
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    Integral of cos^2(x)/sinx

    Hi, I'm new here. I had a question on the thought process for this integral. I know what the answer is, I just don't see how to get to a certain step. The question is:

    <br />
\int \frac {cos^2x}{sinx}dx<br />

    I checked the steps on wolframalpha, which said to rewrite the integral as:

    \int cos(x)cot(x)dx

    Okay, I understand that, but then it says to rewrite that integral as:

    \int csc(x) - sin(x)dx

    I don't understand this last step. Is there an identity that I'm not seeing? Any help is appreciated.
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  2. #2
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    Quote Originally Posted by Shananay View Post
    Hi, I'm new here. I had a question on the thought process for this integral. I know what the answer is, I just don't see how to get to a certain step. The question is:

    <br />
\int \frac {cos^2x}{sinx}dx<br />

    I checked the steps on wolframalpha, which said to rewrite the integral as:

    \int cos(x)cot(x)dx

    Okay, I understand that, but then it says to rewrite that integral as:

    \int csc(x) - sin(x)dx

    I don't understand this last step. Is there an identity that I'm not seeing? Any help is appreciated.
    I would ignore the first step.

    \frac{\cos ^2 x}{\sin{x}} = \frac{1-\sin ^2 x}{\sin{x}} = \frac{1}{\sin{x}} - \sin{x}
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  3. #3
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    Quote Originally Posted by pomp View Post
    I would ignore the first step.

    \frac{\cos ^2 x}{\sin{x}} = \frac{1-\sin ^2 x}{\sin{x}} = \frac{1}{\sin{x}} - \sin{x}
    Ah perfect. Thank you.
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