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JEE Main 201510 AprilOnline
Exam
JEE Main
Year
2015
Date
10 April
Mode
Online
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main 2015 · 10 April · Online · Mathematics · Inverse Trigonometric Functions

If f (x) = 2 ^ - 1 x + ^ - 1 ( 2x 1 + x ^ 2 ), x > 1 , then f(5) is...

If ff\left(x\right) = 2\tan^{- 1}x + \sin^{- 1}(2x1+x2),x>1\left(\dfrac{2x}{1 + {x}^{2}}\right), x > 1, then f(5)f\left(5\right) is equal to

Options

  1. Aπ2\dfrac{\pi}{2}
  2. Btan⁡−1(65156)\tan^{- 1}\left(\dfrac{65}{156}\right)
  3. Cπ\pi
  4. D4tan⁡−1(5)4\tan^{- 1}\left(5\right)

Correct answer

C. π\pi

Step-by-step solution

Substitute tan⁡−1x=θ,θ∈(π4,π2)</p><p>Hence\tan^{- 1}x = \theta, \theta \in \left(\dfrac{\pi}{4}, \dfrac{\pi}{2}\right)</p><p>Hencef\left(x\right) = 2\theta + \sin^{- 1}\left(\sin 2\theta\right)</p><p></p><p>= 2\theta + \pi - 2\theta,as(θ>π4), as \left(\theta > \dfrac{\pi}{4}\right)

=π= \pi

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