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NDA 2023 Maths · Mathematics · Inverse Trigonometric Functions · easy

For principal values: 1. tan ^-1(-1)=-(π)/(4). 2. cos ^-1(-1/2)=-(π)/(3).

Single correct option

Consider the following statements for principal values:
1. tan⁡−1(−1)=−π4\tan^{-1}(-1)=-\dfrac\pi4.
2. cos⁡−1(−12)=−π3\cos^{-1}\left(-\dfrac12\right)=-\dfrac\pi3.
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 principal range of tan⁡−1\tan^{-1} is (−π2,π2)\left(-\frac\pi2,\frac\pi2\right), so tan⁡−1(−1)=−π4\tan^{-1}(-1)=-\frac\pi4 is correct. The range of cos⁡−1\cos^{-1} is [0,π][0,\pi], so it can never be negative; cos⁡−1(−12)=2π3\cos^{-1}\left(-\frac12\right)=\frac{2\pi}3. Only statement 1 is correct.
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Original question written in the NDA 2023 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