Question: All $x$ satisfying the inequality
$\left(\cot ^{-1} x\right)^{2}-7\left(\cot ^{-1} x\right)+10>0$, lie in the interval:-
$(-\infty, \cot 5) \cup(\cot 4, \cot 2)$
$(\cot 5, \cot 4)$
$(\cot 2, \infty)$
$(-\infty, \cot 5) \cup(\cot 2, \infty)$
Correct Option: , 4
Solution:
$\cot ^{-1} x>5, \quad \cot ^{-1} x<2$
$\Rightarrow x<\cot 5, x>\cot 2$
