Match List I with List II, LIST I, LIST II, A. ^(-1) x + ^(-1) x, x [-1,1], I. -()/2, B. ^(-1) √3 - ^(-1)(-√3), II. -()/6, C. ^(-1)((13)/6), III. ()/2, D. ^(-1)(-1/2), IV. ()/6, Choose the correct answer from the options given below: Option 1: A-III, B-I, C-IV, D-II Option 2: A-IV, B-I, C-II, D-III Option 3: A-II, B-III, C-IV, D-I Option 4: A-I, B-II, C-III, D-IV

Answer: A-III, B-I, C-IV, D-II. Solution: A: ^(-1)x + ^(-1)x = ()/2 (III). B: ^(-1)√3 - ^(-1)(-√3) = ()/3 - (5)/6 = -()/2 (I). C: (13)/6 = ()/6, so ^(-1)((13)/6) = ()/6 (IV). D: ^(-1)(-1/2) = -()/6 (II).

Geometry

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Medium

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Match List I with List II

LIST I LIST II
A. $\sin^{-1} x + \cos^{-1} x, x \in [-1,1]$ I. $-\frac{\pi}{2}$
B. $\tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3})$ II. $-\frac{\pi}{6}$
C. $\cos^{-1}\left(\cos\frac{13\pi}{6}\right)$ III. $\frac{\pi}{2}$
D. $\sin^{-1}\left(-\frac{1}{2}\right)$ IV. $\frac{\pi}{6}$

Choose the correct answer from the options given below:

LIST I	LIST II
A. $\sin^{-1} x + \cos^{-1} x, x \in [-1,1]$	I. $-\frac{\pi}{2}$
B. $\tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3})$	II. $-\frac{\pi}{6}$
C. $\cos^{-1}\left(\cos\frac{13\pi}{6}\right)$	III. $\frac{\pi}{2}$
D. $\sin^{-1}\left(-\frac{1}{2}\right)$	IV. $\frac{\pi}{6}$

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

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

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

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

✅ Correct Option: 1

A: $\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}$ (III).

B: $\tan^{-1}\sqrt{3} - \cot^{-1}(-\sqrt{3}) = \frac{\pi}{3} - \frac{5\pi}{6} = -\frac{\pi}{2}$ (I).

C: $\cos\frac{13\pi}{6} = \cos\frac{\pi}{6}$ , so $\cos^{-1}(\cos\frac{13\pi}{6}) = \frac{\pi}{6}$ (IV).

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

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

2022: 17 Aug Shift 2

The value of $\sin\left[\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]$ 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:

2026: 30 May Shift 1

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

2022: 16 July Shift 2

The graph of $\sin^{-1} x$ is represented by:

Solution

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