The set of all the values of $ x $ satisfying the inequality $ \left(\cot ^{-1} x\right)^{2}-7\left(\cot ^{-1} x\right)+100 $ is

Question

The set of all the values of $ x $ satisfying the inequality $ \left(\cot ^{-1} x\right)^{2}-7\left(\cot ^{-1} x\right)+10>0 $ is, $ (-\infty, \cot 5) \cup(\cot 4, \cot 2) $, $ (\cot 5, \cot 4) $, $ (-\infty, \cot 5) \cup(\cot 2, \infty) $, $ (\cot 2, \infty) $

MARKS App · Accepted Answer

We have, cot - 1 x 2 - 7 cot - 1 x + 10 > 0 ⇒ cot - 1 x - 5 cot - 1 x - 2 > 0 ⇒ cot - 1 x ∈ - ∞ , 2 ∪ 5 , ∞ . . . 1 But, cot - 1 x ∈ 0 , π . . . 2 Taking intersection of 1 and 2 we get, ⇒ cot - 1 x ∈ 0,2 ⇒ x ∈ cot 2 , ∞

Search any question & find its solution

Looking for more such questions to practice?