Match List - I with List - II.

List - I	List - II
(A) Range of $y = \text{cosec}^{-1}x$	(I) $R - (-1, 1)$
(B) Domain of $\sec^{-1}x$	(II) $(0, \pi)$
(C) Domain of $\sin^{-1}x$	(III) $[-1, 1]$
(D) Range of $y = \cot^{-1}x$	(IV) $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] - \{0\}$

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Match List-I with List-II

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

The simplified form of $\tan^{-1}\left(\frac{\cos x}{1+\sin x}\right)$, $-\frac{\pi}{2} < x < \frac{\pi}{2}$ is

The value of $\tan\left(\dfrac{1}{2}\cos^{-1}\dfrac{\sqrt5}{3}\right)$ is equal to

Consider $f(x) = \sin(3x) + 4, \forall x \in \mathbb{R}$. Then

(A) Maximum value of $f(x)$ is 5

(B) Minimum value of $f(x)$ is 3

(C) Maximum value of $f(x)$ is attained at $x = \frac{\pi}{6}$

(D) Minimum value of $f(x)$ is attained at $x = 0$

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