Question

Evaluate : $\int \frac{\sin x}{\sin (x-a)}dx$.

Answer 1

$\int \frac{\sin x}{\sin (x-a)}dx$

$=\int \frac{\sin (x-a+a)}{\sin (x-a)}dx$

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

$=\int \cos adx+\sin a\int \cot (x-a)dx$

$=x\cos a+\sin a.\ln |\sin (x-a)|$