Question

Evaluate :

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

Answer 1

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

$I=\int \frac{\sin x\cos a-\cos x\sin a}{\sin x}dx$

$I=\int \cos adx-\int \sin a\cot xdx$

$I=\cos a\int 1.dx-\sin a\int \cot xdx$

$I=x\cos a-\sin a\log |\sin x|+C$