We can derive reduction formulas for the integral of the form \( \i...
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We can derive reduction formulas for the integral of the form \( \int \sin ^{n} x d x, \int \cos ^{n} x d x \int \tan ^{n} x d x \), \( \int \cot ^{n} x d x \) and other integrals of these form using integration by parts. In turn these reduction formulas can be used to compute integrals of higher power of \( \sin x, \cos x \) etc.
If \( \int \operatorname{cosec}^{n} x d x=\frac{-\operatorname{cosec}^{n-2} x \cot x}{n-1}+ \)
\( A \int \operatorname{cosec}^{n-2} x d x \) then \( A \) is equal to
(a) \( \frac{1}{n-2} \)
(b) \( \frac{n}{n-2} \)
(c) \( \frac{n-1}{n-2} \)
(d) \( \frac{n-2}{n-1} \)
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