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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 x satisfies the inequality (tan^ - 1 x) ^ 2 + 3(tan^ - 1 x) - 4...

If xx satisfies the inequality (tan−1x)2+3(tan−1x)−4>0{\left(tan^{- 1}x\right)}^{2} + 3\left(tan^{- 1}x\right) - 4 > 0, then the complete set of values of xx is

Options

  1. A(−tan⁡4,π4)\left(- \tan 4, \dfrac{\pi}{4}\right)
  2. B\left(- \infty,\tan 4\right) \cup (π4,∞)\left(\dfrac{\pi}{4}, \infty\right)
  3. C(tan⁡1,∞)\left(\tan 1,\infty\right)
  4. D(tan⁡4,tan⁡1)\left(\tan 4,\tan 1\right)

Correct answer

C. (tan⁡1,∞)\left(\tan 1,\infty\right)

Step-by-step solution

Let, tan−1x=ttan^{- 1}x = t

the given inequality becomes t2+3t−4>0⇒(t+4)(t−1)>0t^{2} + 3t - 4 > 0 ⇒ \left(t + 4\right)\left(t - 1\right) > 0
∴t<−4∴ t < - 4 or t>1t > 1
tan−1x<−4tan^{- 1}x < - 4 (not possible) or tan−1x>1tan^{- 1}x > 1
⇒x>tan⁡1⇒ x > \tan 1

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