If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is

  • [JEE MAIN 2021]
  • A

    $2 \sqrt{3}$

  • B

    $\frac{3}{2}$

  • C

    $\sqrt{3}$

  • D

    $\frac{1}{2}$

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