The value of $\mathrm{s}\mathrm{i}\mathrm{n}\left\{{\mathrm{c}\mathrm{o}\mathrm{t}}^{-1}\left[\mathrm{c}\mathrm{o}\mathrm{s}\left({\mathrm{c}\mathrm{o}\mathrm{t}}^{-1}\left(\frac{1}{x}\right)\right)\right]\right\}$ is equal to $\left(x>0\right)$

• Correct answer
  A

  $\sqrt{\frac{1+x^2}{2+x^2}}$
• B

  $\sqrt{\frac{1-x^2}{2+x^2}}$
• C

  $\sqrt{\frac{1+x^2}{2-x^2}}$
• D

  $\sqrt{\frac{2+x^2}{1+x^2}}$

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