IAT (IISER) 2025 | Inverse Trigonometric Functions Question 1 | Mathematics

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?

$f$ is decreasing for $x>0$

$f$ is decreasing for $x<0$

$f$ is decreasing on $\mathbf{R}$

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

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