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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int \large\frac{\sin x}{\sin (x-\alpha)}$$dx$

\[\begin {array} {1 1} (a)\;x \cos \alpha + \sin \alpha \log | \sin (x - \alpha)| +c \\ (b)\;x \cos \alpha + \sin \alpha +c \\ (c)\;x \sin \alpha + \sin \alpha \log | \sin (x - \alpha)| +c\\ (d)\;None \end {array}\]

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A)
=> $\int \large\frac{\sin (x - \alpha + \alpha)}{\sin (x - \alpha)}$$dx$
=> $\int \large\frac{\sin (x - \alpha) \cos \alpha}{\sin (x - \alpha)}+ \int \large\frac{\sin \cos (x - \alpha)}{\sin (x - \alpha)}$
=> $ \int \cos \alpha .dx + \int \sin \alpha \cot (x- \alpha)dx$
$x \cos \alpha + \sin \alpha \log | \sin (x - \alpha)| +c$
Hence a is the correct answer.
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