Match the LIST-I with LIST-II, LIST-I Functions, LIST-II Principal value, A. ^(-1)(1/2), I. ()/4, B. ^(-1)(-1/√2), II. ()/6, C. ^(-1)(1), III. -()/4, D. ^(-1)(-1/2), IV. (2)/3, Choose the correct answer from the options given below: Option 1: A-I, B-IV, C-II, D-III Option 2: A-II, B-III, C-I, D-IV Option 3: A-IV, B-I, C-III, D-II Option 4: A-III, B-IV, C-II, D-I

Answer: A-II, B-III, C-I, D-IV. Solution: Using principal value branches: ^(-1)(1/2) = /6 (II). ^(-1)(-1/√2) = -/4 (III), since the range is [-/2,/2]. ^(-1)(1) = /4 (I). ^(-1)(-1/2) = - /3 = 2/3 (IV), since the range is [0,].

Geometry

Trigonometry

Easy

core

Match the LIST-I with LIST-II

LIST-I Functions LIST-II Principal value
A. $\sin^{-1}\left(\dfrac{1}{2}\right)$ I. $\dfrac{\pi}{4}$
B. $\sin^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$ II. $\dfrac{\pi}{6}$
C. $\tan^{-1}(1)$ III. $-\dfrac{\pi}{4}$
D. $\cos^{-1}\left(-\dfrac{1}{2}\right)$ IV. $\dfrac{2\pi}{3}$

Choose the correct answer from the options given below:

LIST-I Functions	LIST-II Principal value
A. $\sin^{-1}\left(\dfrac{1}{2}\right)$	I. $\dfrac{\pi}{4}$
B. $\sin^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$	II. $\dfrac{\pi}{6}$
C. $\tan^{-1}(1)$	III. $-\dfrac{\pi}{4}$
D. $\cos^{-1}\left(-\dfrac{1}{2}\right)$	IV. $\dfrac{2\pi}{3}$

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

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

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

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

✅ Correct Option: 2

Using principal value branches:

$\sin^{-1}(1/2) = \pi/6$ (II).

$\sin^{-1}(-1/\sqrt{2}) = -\pi/4$ (III), since the range is $[-\pi/2,\pi/2]$ .

$\tan^{-1}(1) = \pi/4$ (I).

$\cos^{-1}(-1/2) = \pi - \pi/3 = 2\pi/3$ (IV), since the range is $[0,\pi]$ .

2023: 23 May Shift 3

The simplest form of $\tan^{-1}\left\{\frac{x}{\sqrt{a^2 - x^2}}\right\}$ is, where $-a < x < a$ .

2022: 4 Aug Shift 1

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

2025: 22 May Shift 1

The minimum value of the function $f(x) = 3\sin x - 4\cos x, x \in [-4\pi, 4\pi]$ is equal to

2022: 23 Aug Shift 1

$\sin^{-1}(\cos x) = \frac{\pi}{2} - x$ is valid for :

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) $\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$	(I) $\frac{3\pi}{4}$
(B) $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$	(II) $-\frac{\pi}{3}$
(C) $\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)$	(III) $\frac{\pi}{2}$
(D) $\cos^{-1}\left(\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right)$	(IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below :

2023: 23 May Shift 3

The maximum value of $\sin x + \cos x, x \in R$ is:

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