$\operatorname{Sech}^{-1}(\sin \alpha)=$

• A

  $\log \left(\sin \alpha+\sqrt{\sin ^2 \alpha-1}\right)$
• B

  $\log (\tan \alpha+1)$
• Correct answer
  C

  $\log \left(\cot \frac{\alpha}{2}\right)$
• D

  $\log \left(\frac{1+\tan \alpha}{2 \sin \alpha}\right)$

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