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NDA 2020 Maths · Mathematics · Inverse Trigonometric Functions · medium

The function tan ^-1x is increasing on the whole real line. 2. The function sin ^-1x is an even function on [-1,1].

Single correct option

Consider the following statements:
1. The function tan⁡−1x\tan^{-1}x is increasing on the whole real line.
2. The function sin⁡−1x\sin^{-1}x is an even function on [−1,1][-1,1].
Which of the statements given above 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

The derivative of tan⁡−1x\tan^{-1}x is 11+x2>0\frac1{1+x^2}>0, so statement 1 is correct. For sin⁡−1\sin^{-1} we have sin⁡−1(−x)=−sin⁡−1x\sin^{-1}(-x)=-\sin^{-1}x, so it is an odd function, not even; statement 2 is wrong (e.g. sin⁡−1(−1)=−π2≠π2\sin^{-1}(-1)=-\frac\pi2\ne\frac\pi2).
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Original question written in the NDA 2020 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