If $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2x}} dx=a{\sin }^{-1}\left(\frac{\sin x+\cos x}{ b}\right)+c,$ where $c$ is a constant of integration, then the ordered pair $\left(a,b\right)$ is equal to:

• A

  $\left(1,-3\right)$
• B

  $\left(3,1\right)$
• C

  $\left(-1,3\right)$
• Correct answer
  D

  $\left(1,3\right)$

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