If a real valued function $f(x)=\left\{\begin{array}{cc}(1+\sin x)^{\operatorname{cosec} x}, & -\pi / 2 < x < 0 \\ a, & x=0 \\ \frac{e^{2 / x}+e^{3 / x}}{a e^{2 / x}+b e^{3 / x}}, & 0 < x < \pi / 2\end{array}\right.$, is continuous at $\mathrm{x}=0$, then $\mathrm{ab}=$

• A

  e
• B

  $\mathrm{e}^2$
• Correct answer
  C

  1
• D

  $-1$

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