If $f(x)=\left\{\begin{array}{cll}\frac{\left(e^{a x}-1\right) \log (1+x)}{\sin ^2 x} &, & \text { if } x>0 \\ 2 &, & \text { if } x=0 \\ \frac{\cos 4 x-\cos b x}{\tan ^2 x} &, & \text { if } x < 0\end{array}\right.$ is continuous at $\mathrm{x}=0$ then $\sqrt{\mathrm{b}^2-\mathrm{a}^2}=$

• Correct answer
  A

  $4$
• B

  $5$
• C

  $3$
• D

  $7$

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