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NDA 2021 Maths · Mathematics · Inverse Trigonometric Functions · medium

Tan ^-1x+cot ^-1x=(π)/(2) for every real x. 2. The principal value branch of tan ^-1x is [0,π].

Single correct option

Which of the statements is/are correct? 1. tan⁡−1x+cot⁡−1x=π2\tan^{-1}x+\cot^{-1}x=\dfrac\pi2 for every real xx. 2. The principal value branch of tan⁡−1x\tan^{-1}x is [0,π][0,\pi].
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

Statement 1 is a standard identity valid for all real xx with cot⁡−1x∈(0,π)\cot^{-1}x\in(0,\pi). The principal branch of tan⁡−1x\tan^{-1}x is the open interval (−π2,π2)\left(-\dfrac\pi2,\dfrac\pi2\right), so statement 2 is false. Only 1 is correct.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake