Match the LIST-I with LIST-II, LIST-I (Function), LIST-II (Range of the principal value branch), A. ^(-1)x, I. (-()/2, ()/2), B. cosec^(-1)x, II. (0, ), C. ^(-1)x, III. [0, ], D. ^(-1)x, IV. [-()/2, ()/2] - \0\, Choose the correct answer from the options given below: Option 1: A-II, B-I, C-III, D-IV Option 2: A-III, B-IV, C-I, D-II Option 3: A-III, B-II, C-IV, D-I Option 4: A-II, B-IV, C-I, D-III

Answer: A-III, B-IV, C-I, D-II. Solution: Standard principal value branches: ^(-1)x gives [0,] (III), cosec^(-1)x gives [-/2,/2] excluding 0 (IV), ^(-1)x gives (-/2,/2) (I), and ^(-1)x gives (0,) (II).

Geometry

Trigonometry

Easy

core

Match the LIST-I with LIST-II

LIST-I (Function) LIST-II (Range of the principal value branch)
A. $\cos^{-1}x$ I. $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$
B. $\text{cosec}^{-1}x$ II. $(0, \pi)$
C. $\tan^{-1}x$ III. $[0, \pi]$
D. $\cot^{-1}x$ IV. $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right] - \{0\}$

Choose the correct answer from the options given below:

LIST-I (Function)		LIST-II (Range of the principal value branch)
A. $\cos^{-1}x$		I. $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$
B. $\text{cosec}^{-1}x$		II. $(0, \pi)$
C. $\tan^{-1}x$		III. $[0, \pi]$
D. $\cot^{-1}x$		IV. $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right] - \{0\}$

A-II, B-I, C-III, D-IV

A-III, B-IV, C-I, D-II

A-III, B-II, C-IV, D-I

A-II, B-IV, C-I, D-III

✅ Correct Option: 2

Standard principal value branches: $\cos^{-1}x$ gives $[0,\pi]$ (III), $\text{cosec}^{-1}x$ gives $[-\pi/2,\pi/2]$ excluding $0$ (IV), $\tan^{-1}x$ gives $(-\pi/2,\pi/2)$ (I), and $\cot^{-1}x$ gives $(0,\pi)$ (II).

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $\tan^{-1}\frac{2}{11} + \tan^{-1}\frac{7}{24}$	(I) $\frac{3\pi}{4}$
(B) $\tan^{-1}2 + \tan^{-1}3$	(II) $\pi$
(C) $\tan^{-1}1 + \tan^{-1}2 + \tan^{-1}3$	(III) $\tan^{-1}\frac{1}{2}$
(D) $\tan^{-1}\frac{1}{7} + \tan^{-1}\frac{1}{13}$	(IV) $\tan^{-1}\frac{2}{9}$

Choose the correct answer from the options given below:

2025: 26 May Shift 2

Arrange the principal values of the following functions in ascending order

(A) $\cosec^{-1}(2)$

(B) $\tan^{-1}(-\sqrt{3})$

(D) $\tan^{-1}\left(\cos\frac{3\pi}{7}\right)$

Choose the correct answer from the options given below:

2022: 10 Aug Shift 1

$\tan(\alpha + \beta) =$

2025: 16 May Shift 1

Match List-I with List-II

List-I	List-II
Inverse Trigonometric function	Principal values of arguments
(A) $sin^{-1}\left(\frac{-1}{2}\right)$	(I) $\frac{-\pi}{3}$
(B) $cos^{-1}\left(\frac{-1}{2}\right)$	(II) $\frac{3\pi}{4}$
(C) $tan^{-1}(-\sqrt{3})$	(III) $\frac{-\pi}{6}$
(D) $sec^{-1}(-\sqrt{2})$	(IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

2023: 23 May Shift 3

The principal value of $\cot^{-1}\left(-\frac{1}{\sqrt{3}}\right)$

2025: 22 May Shift 1

The value of $\tan^2(\sec^{-1} 2) + \cot^2(\cosec^{-1} 3)$ is equal to

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