Match List-I with List-II
| List-I | List-II | ||
| (A) | The range of \( \sin^{-1}x \) | (I) | \( [-1,1] \) |
| (B) | Domain of \( \cos^{-1}x \) | (II) | \( (-\infty,\infty) \) |
| (C) | The range of \( \tan^{-1}x \) | (III) | \( \left[-\displaystyle\frac{\pi}{2},\frac{\pi}{2}\right] \) |
| (D) | Domain of \( \tan^{-1}x \) | (IV) | \( \left(-\displaystyle\frac{\pi}{2},\frac{\pi}{2}\right) \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
The domain of an inverse trigonometric function is the range of the original function, and its range is the principal-value branch.
(A) The range of \( \sin^{-1}x \)
This matches (III) \( \left[-\frac{\pi}{2},\frac{\pi}{2}\right] \), the principal-value branch of \( \sin^{-1} \); both end points are included, since \( \sin^{-1}(\pm 1)=\pm\frac{\pi}{2} \).
(B) Domain of \( \cos^{-1}x \)
This matches (I) [−1, 1], because cos x takes only values from −1 to 1.
(C) The range of \( \tan^{-1}x \)
This matches (IV) \( \left(-\frac{\pi}{2},\frac{\pi}{2}\right) \). The end points are excluded because tan x is not defined at \( \pm\frac{\pi}{2} \).
(D) Domain of \( \tan^{-1}x \)
This matches (II) \( (-\infty,\infty) \), because tan x takes every real value.
So the matching is (A)-(III), (B)-(I), (C)-(IV), (D)-(II).
NCERT (2026-27 edition):
Basic Concepts
