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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

If ( ^ -1 x) ^ 2 - 7( ^ -1 x) + 10 > 0 , then the range of x will be

If (cot⁡−1x)2−7(cot⁡−1x)+10>0{\left(\cot^{-1} x\right)}^{2} - 7\left(\cot^{-1} x\right) + 10 > 0, then the range of xx will be

Options

  1. A(−∞,cot⁡2)( - \infty, \cot 2 )
  2. B(−∞,cot⁡5)\left(- \infty, \cot 5\right)
  3. C(cot⁡2,cot⁡5)\left(\cot 2, \cot 5\right)
  4. D(cot⁡2,∞)\left(\cot 2, \infty\right)

Correct answer

D. (cot⁡2,∞)\left(\cot 2, \infty\right)

Step-by-step solution

(cot⁡−1x−5)(cot⁡−1x−2)>0\left(\cot^{-1} x - 5\right)\left(\cot^{-1} x - 2\right) >0

⇒cot⁡−1x∈(−∞,2)∪(5,∞)<⇒ \cot^{-1} x \in \left(- \infty,2\right)\cup \left(5, \infty\right)< br />
⇒cot⁡−1x∈(0,2)(Takingintersectionwith⇒ \cot^{-1} x \in \left(0, 2\right)(Taking intersection withrange of \cot^{-1} x)<br/><br/>)<br /><br />⇒ n \in ( \cot 2, \infty )
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