Let $g:[0, \infty) \rightarrow \mathbb{R}$ be a continuous function such that $g(x)+(\log 2) \int_0^x g(t) \cos t d t=1$ Then the value of $g\left(\frac{\pi}{6}\right)$ is

• Correct answer
  A

  $\frac{1}{\sqrt{2}}$
• B

  $\sqrt{2}$
• C

  $\frac{\sqrt{3}}{2}$
• D

  $\frac{1}{2}$

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