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NDA 2017 Maths · Mathematics · Inverse Trigonometric Functions · medium

Tan ^-1x+cot ^-1x=(π)/(2) for every real number x. 2. sin (sin ^-1x)=x for every real number x.

Single correct option

Consider the following statements.

1. tan⁡−1x+cot⁡−1x=π2\tan^{-1}x+\cot^{-1}x=\dfrac\pi2 for every real number xx.
2. sin⁡(sin⁡−1x)=x\sin(\sin^{-1}x)=x for every real number xx.

Which of the statements is/are correct?
  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 true: for all real xx the principal values satisfy tan⁡−1x+cot⁡−1x=π2\tan^{-1}x+\cot^{-1}x=\frac\pi2. Statement 2 is false: sin⁡−1x\sin^{-1}x exists only for x∈[−1,1]x\in[-1,1], so sin⁡(sin⁡−12)\sin(\sin^{-1}2) is undefined. Only statement 1 is correct.
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Original question written in the NDA 2017 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