Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function given by $f(x)=\cos \left(\tan ^{-1} x\right)$. Which one of the following statements is TRUE?

• Correct answer
  A

  $\quad f$ is decreasing for $x\gt0$
• B

  $\quad f$ is decreasing for $x \lt 0$
• C

  $\quad f$ is decreasing on $\mathbf{R}$
• D

  $\quad f$ is decreasing on the interval $(-1,1)$

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