Question:
\(\displaystyle \int \sin^{3}\theta\ \csc^{2}\theta\,d\theta=\ \ ?\)
\(\displaystyle \int \sin^{3}\theta\ \csc^{2}\theta\,d\theta=\ \ ?\)
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Rewrite reciprocals ($\csc^2=1/\sin^2$) and cancel powers first.
Updated On: Oct 17, 2025
- \(c+\theta\)
- \(c+\cos\theta\)
- \(c-\cos\theta\)
- \(c+\sin\theta\)
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The Correct Option is C
Solution and Explanation
\(\csc^{2}\theta=\dfrac{1}{\sin^{2}\theta}\). So
\[
\sin^{3}\theta\cdot\csc^{2}\theta=\sin^{3}\theta\cdot\frac{1}{\sin^{2}\theta}=\sin\theta.
\]
Then \(\int \sin\theta\,d\theta=-\cos\theta+c\).
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