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JEE Main 201419 AprilOnline
Exam
JEE Main
Year
2014
Date
19 April
Mode
Online
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main 2014 · 19 April · Online · Mathematics · Inverse Trigonometric Functions

The principal value of ^ - 1 (cot(43π)/(4)) is

The principal value of tan⁡−1(cot43π4)\tan^{- 1}\left(cot\dfrac{43\pi}{4}\right) isThe principal value of ^ - 1 (cot(43π)/(4)) is

Options

  1. Aπ4\dfrac{\pi}{4}
  2. B−π4- \dfrac{\pi}{4}
  3. C3π4\dfrac{3\pi}{4}
  4. D- \dfrac{3 π}{4}

Correct answer

B. −π4- \dfrac{\pi}{4}

Step-by-step solution

−π2<tan⁡−1x<π2\dfrac{- \pi}{2} < \tan^{- 1}x < \dfrac{\pi}{2}

The principal value of ^ - 1 (cot(43π)/(4)) is

cot⁡(43π4)=cot⁡(10π+3π4)\cot \left(\dfrac{43\pi}{4}\right) = \cot \left(10\pi + \dfrac{3\pi}{4}\right)

=cot3π4= cot\dfrac{3\pi}{4}

=−1= - 1

tan⁡−1cot⁡(43π4)=tan⁡−1(−1)\tan^{- 1}\cot \left(\dfrac{43\pi}{4}\right) = \tan^{- 1}\left(- 1\right)

=−π4= - \dfrac{\pi}{4}

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