# All x satisfying the inequality

Question:

All $x$ satisfying the inequality

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

1. $(-\infty, \cot 5) \cup(\cot 4, \cot 2)$

2. $(\cot 5, \cot 4)$

3. $(\cot 2, \infty)$

4. $(-\infty, \cot 5) \cup(\cot 2, \infty)$

Correct Option: , 4

Solution:

$\cot ^{-1} x>5, \quad \cot ^{-1} x<2$

$\Rightarrow x<\cot 5, x>\cot 2$