Match List-I with List-II

Choose the correct answer from the options given below:

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

The correct answer is Option (1) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Principal value ranges:

$\sin^{-1}x \in \left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

$\cos^{-1}x \in \left[0,\pi\right]$

$\tan^{-1}x \in \left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

$\sec^{-1}x \in \left[0,\pi\right]\setminus\left\{\frac{\pi}{2}\right\}$

1. $\sin^{-1}\left(-\frac12\right)$

$\sin\left(-\frac{\pi}{6}\right)=-\frac12$

$ \sin^{-1}\left(-\frac12\right)=-\frac{\pi}{6}$

Matches (III)

2. $\cos^{-1}\left(-\frac12\right)$

$\cos\left(\frac{2\pi}{3}\right)=-\frac12$

$\ \cos^{-1}\left(-\frac12\right)=\frac{2\pi}{3}$

Matches (IV)

3. $\tan^{-1}\left(-\sqrt3\right)$

$\tan\left(-\frac{\pi}{3}\right)=-\sqrt3$

$\ \tan^{-1}\left(-\sqrt3\right)=-\frac{\pi}{3}$

Matches (I)

4. $\sec^{-1}\left(-\sqrt2\right)$

$\sec\left(\frac{3\pi}{4}\right)=-\sqrt2$

$ \sec^{-1}\left(-\sqrt2\right)=\frac{3\pi}{4}$

Matches (II)