The principal value of ^(-1)(-1/√3) Option 1: ()/3 Option 2: -()/6 Option 3: 1/√3 Option 4: (2)/3

Answer: (2)/3. Solution: Range of ^(-1) is (0, ). We need angle in this range with = -1/√3. Now (2/3) = (2/3)/(2/3) = (-1/2)/(√3/2) = -1/√3. So ^(-1)(-1/√3) = 2/3.

Geometry

Trigonometry

Easy

core

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

$\frac{\pi}{3}$

$-\frac{\pi}{6}$

$\frac{1}{\sqrt{3}}$

$\frac{2\pi}{3}$

✅ Correct Option: 4

Range of $\cot^{-1}$ is $(0, \pi)$ . We need angle in this range with $\cot\theta = -1/\sqrt{3}$ . Now $\cot(2\pi/3) = \cos(2\pi/3)/\sin(2\pi/3) = (-1/2)/(\sqrt{3}/2) = -1/\sqrt{3}$ . So $\cot^{-1}(-1/\sqrt{3}) = 2\pi/3$ .

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:

2026: 29 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	If $\cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi$ then $\alpha(2\beta+\gamma) + \beta(2\gamma+\alpha) + \gamma(2\alpha+\beta)$ equals	I.	$1$
B.	The value of $\tan^2(\sec^{-1}4) + \cot^2(\text{cosec}^{-1}5)$ is	II.	$9$
C.	If $\sin\left(\cos^{-1}\dfrac{2}{5} + \sin^{-1}x\right) = 1$ then $10x$ equals	III.	$4$
D.	The length of the interval of domain of $\sin^{-1}2x$ is	IV.	$39$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

Let $\tan^{-1}y = \tan^{-1}x + \tan^{-1}\left(\frac{2x}{1-x^2}\right)$ . Then $y$ is :

2022: 30 Aug Shift 1

$\sin^{-1}(1 - x) - 2\sin^{-1}x = \frac{\pi}{2}$ , than $x$ is equal to

(a) $0$

(b) $1$

(d) $2$

Choose the most appropriate answer from the options given below:

2022: 4 Aug Shift 1

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

2025: 13 May Shift 2

Match List-I with List-II

List-I	List-II
(A) $\sin^{-1}(-1)$	(I) $\frac{5\pi}{6}$
(B) $\cot^{-1}(-1)$	(II) $\frac{-\pi}{2}$
(C) $\sec^{-1}\left(\frac{-2}{\sqrt{3}}\right)$	(III) $\frac{\pi}{4}$
(D) $\tan^{-1}(1)$	(IV) $\frac{3\pi}{4}$

Choose the correct answer from the options given below:

The principal value of cot⁡−1(−13)\cot^{-1}\left(-\frac{1}{\sqrt{3}}\right)cot−1(−3​1​)

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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