Solve $c o s^{- 1} x > c o s^{- 1} x^{2}$ .

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Solution

${cos}^{- 1} x > {cos}^{- 1} x^{2}$
We know that ${cos}^{- 1}$ is a decreasing function
$∴ x < x^{2}$
$\Rightarrow x^{2} - x > 0$
$\Rightarrow x (x - 1) > 0$
$\Rightarrow x \in (- \infty, 0) \cup [1, \infty)$
Domain of ${cos}^{- 1} x$ is $[- 1, 1]$
$∴ x [- 1, 0)$

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