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$\int \frac{\cos (x - a)}{\sin x} d x =$

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$\cos a \log | \sin x | - x \sin a + c$

$\cos a \log | \sin x | + x \sin a + c$

$\cos a \log | \sin x | + x \tan a + c$

answer is B.

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Detailed Solution

$\begin{array}{l} \int \frac{\cos (x - a)}{\sin x} d x = \int \frac{\cos x \cos a + \sin x \sin a}{\sin x} d x = \int (\cos a \cdot \cot x + \sin a) d x \\ = \cos a \cdot \log | \sin x | + x \cdot \sin a + c \end{array}$

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