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Integrate the Function Sin(x-a)/Sin(x+a)

$I = \int \frac{\sin (x - a)}{\sin (x + a)} d x = \int \frac{\sin (x - a + a - a)}{\sin (x + a)} d x = \int \frac{\sin {(x + a) - 2 a}}{\sin (x + a)} d x = \int \frac{\sin (x + a) \cos 2 a - \cos (x + a) \sin 2 a}{\sin (x + a)} d x = \int \cos 2 a d x - \int \cot (x + a) \sin 2 a d x = \cos 2 a \int d x - \sin 2 a \int cot (x + a) d x = \cos 2 a \times x - \sin 2 a \log | \sin (x + a) | + c = x \cos 2 a - \sin 2 a \log | \sin (x + a) | + c .$

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