Match List - I with List - II.
| List - I | List - II | ||
| Functions | Range | ||
| (A) | \(\mathrm{cosec}^{-1}x\) | (I) | \((0, \pi)\) |
| (B) | \(\sec^{-1}x\) | (II) | \(\left[\displaystyle\frac{-\pi}{2}, \frac{\pi}{2}\right] - \{0\}\) |
| (C) | \(\tan^{-1}x\) | (III) | \(\left(-\displaystyle\frac{\pi}{2}, \frac{\pi}{2}\right)\) |
| (D) | \(\cot^{-1}x\) | (IV) | \([0, \pi] - \left\{\displaystyle\frac{\pi}{2}\right\}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
The range of each inverse trigonometric function is its principal value branch.
(A) \(\mathrm{cosec}^{-1}x\)
This matches (II) \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] - \{0\}\).
cosec is taken on \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), but 0 is removed because cosec 0 is not defined.
(B) \(\sec^{-1}x\)
This matches (IV) \([0, \pi] - \left\{\frac{\pi}{2}\right\}\).
sec is taken on \([0, \pi]\), but \(\frac{\pi}{2}\) is removed because \(\sec\frac{\pi}{2}\) is not defined.
(C) \(\tan^{-1}x\)
This matches (III) \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\).
The end points are excluded because \(\tan\left(\pm\frac{\pi}{2}\right)\) is not defined.
(D) \(\cot^{-1}x\)
This matches (I) \((0, \pi)\).
The end points are excluded because cot 0 and \(\cot\pi\) are not defined.
NCERT (2026-27 edition):
Basic Concepts
