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:

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

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

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