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NDA 2024 Maths · Mathematics · Inverse Trigonometric Functions · easy

Cos ^-1(-x)=π-cos ^-1x for x∈[-1,1]. 2. tan ^-1x+cot ^-1x=(π)/(2) holds only for x>0.

Single correct option

Which of the statements is/are correct?
1. cos⁡−1(−x)=π−cos⁡−1x\cos^{-1}(-x)=\pi-\cos^{-1}x for x∈[−1,1]x\in[-1,1].
2. tan⁡−1x+cot⁡−1x=π2\tan^{-1}x+\cot^{-1}x=\dfrac\pi2 holds only for x>0x>0.
  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 on the whole domain. For 2, tan⁡−1x+cot⁡−1x=π2\tan^{-1}x+\cot^{-1}x=\frac\pi2 holds for every real xx (with cot⁡−1\cot^{-1} taking values in (0,π)(0,\pi)), so 'only for x>0x>0' is false.
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Original question written in the NDA 2024 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