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  4. All x satisfying the inequality ( cot-1 x)2 - 7 ( cot-1 x)+10 > 0 lie in the interval :

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Q. All $x$ satisfying the inequality $\left(\cot^{-1} x\right)^{2} - 7 \left(\cot^{-1} x\right)+10 > 0 $ lie in the interval :

JEE MainJEE Main 2019Inverse Trigonometric Functions

Solution:

$\cot^{-1}x>5 , \cot^{-1}x <2$
$ \Rightarrow x < \cot5 , x > \cot2 $