Question

Find the following :

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

(b) \(\int\frac{sinx}{sin(x - a)}dx\)

Answer 1

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

= cos 2a ∫ dt – sin 2a ∫ cot t dt

= (cos 2a)^t – sin 2a log | sin t | + C₁

= (x + a) cos 2a – sin 2a log | sin (x + a) | + C₁

= x cos 2a – sin 2a log | sin (x + a) | + a cos 2a + C₁

= x cos 2a – sin 2a log | sin (x + a) | + C

( where C = a cos 2a + C₁)