$\int \frac{\sin (x-a)}{\sin (x-b)} d x=A x+B \log |\sin (x-b)|+C \Rightarrow(A, B)=$

• Correct answer
  A

  $(\cos (b-a), \sin (b-a))$
• B

  $(\cos (b-a), \sin (a-b))$
• C

  $(-\cos (b-a), \sin (b-a))$
• D

  $(-\cos (b-a), \sin (a-b))$

Hence, the correct answer is option: 'A'.