If the extreme value of the function $f(x)=\frac{4}{\sin x}+\frac{1}{1-\sin x}$ in $\left[0, \frac{\pi}{2}\right]$ is $m$ and it exists at $\mathrm{x}=\mathrm{k}$, then $\cos \mathrm{k}=$

• A

  $\frac{\sqrt{\mathrm{m}}}{4}$
• B

  $\frac{\sqrt{\mathrm{m}+1}}{\sqrt{2}}$
• Correct answer
  C

  $\frac{\sqrt{5}}{\sqrt{\mathrm{~m}}}$
• D

  $\frac{1}{\mathrm{~m}}$

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