$\frac{\sqrt{2}-\sin \alpha-\cos \alpha}{\sin \alpha-\cos \alpha}=$

• A

  $\sec \left(\frac{\alpha}{2}-\frac{\pi}{8}\right)$
• B

  $\cos \left(\frac{\pi}{8}-\frac{\alpha}{2}\right)$
• Correct answer
  C

  $\tan \left(\frac{\alpha}{2}-\frac{\pi}{8}\right)$
• D

  $\cot \left(\frac{\alpha}{2}-\frac{\pi}{2}\right)$

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