The value of ^(-1)(3)-^(-1)(-2) is Option 1: ()/3 Option 2: 0 Option 3: -()/3 Option 4: (2)/3

Answer: -()/3. Solution: ^(-1)(3) = ()/3 since the principal range is (-()/2,()/2). ^(-1)(-2) = - ()/3 = (2)/3 since the principal range is [0,]. Difference = ()/3-(2)/3 = -()/3.

Geometry

Trigonometry

Easy

core

The value of $\tan^{-1}(\sqrt3)-\sec^{-1}(-2)$ is

$\dfrac{\pi}{3}$

$-\dfrac{\pi}{3}$

$\dfrac{2\pi}{3}$

✅ Correct Option: 3

$\tan^{-1}(\sqrt3) = \dfrac{\pi}{3}$ since the principal range is $\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$ .

$\sec^{-1}(-2) = \pi - \dfrac{\pi}{3} = \dfrac{2\pi}{3}$ since the principal range is $[0,\pi]$ .

Difference $= \dfrac{\pi}{3}-\dfrac{2\pi}{3} = -\dfrac{\pi}{3}$ .

2023: 23 May Shift 3

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

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:

2022: 25 May Shift 1

Value of $\frac{e^{\sin(\tan^{-1} x + \cot^{-1} x)}}{e^{\sin(\sin^{-1} x + \cos^{-1} x)}}, x \in [-1, 1]$ , is:

2023: 23 May Shift 3

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

2025: 19 May Shift 1

Match List-I with List-II

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

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 :

The value of tan⁡−1(3)−sec⁡−1(−2)\tan^{-1}(\sqrt3)-\sec^{-1}(-2)tan−1(3​)−sec−1(−2) is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\tan^{-1}(\sqrt3)-\sec^{-1}(-2)$ is