If $\{x\}=x-[x]$ where $[x]$ is the greatest integer $\leq x$ and $\lim _{x \rightarrow 0^{-}} \frac{\operatorname{Cos}^{-1}\left(1-\{x\}^2\right) \operatorname{Sin}^{-1}(1-\{x\})}{\{x\}-\{x\}^4}=\theta$, then $\tan \theta=$

• Correct answer
  A

  $\frac{1}{\sqrt{3}}$
• B

  $1$
• C

  $\sqrt{3}$
• D

  $\infty$

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