Match List-I with List-II
|
List-I Inverse Trigonometric Function |
List-II Principal values of arguments |
|
(A) $\sin^{-1}(\frac{-1}{2})$ |
(I) $\frac{-\pi}{3}$ |
|
(B) $\cos^{-1}(\frac{-1}{2})$ |
(II) $\frac{3\pi}{4}$ |
|
(C) $\tan^{-1}(-\sqrt{3})$ |
(III) $\frac{-\pi}{6}$ |
|
(D) $\sec^{-1}(-\sqrt{2})$ |
(IV) $\frac{2\pi}{3}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
|
List-I Inverse Trigonometric Function |
List-II Principal values of arguments |
|
(A) $\sin^{-1}(\frac{-1}{2})$ |
(III) $\frac{-\pi}{6}$ |
|
(B) $\cos^{-1}(\frac{-1}{2})$ |
(IV) $\frac{2\pi}{3}$ |
|
(C) $\tan^{-1}(-\sqrt{3})$ |
(I) $\frac{-\pi}{3}$ |
|
(D) $\sec^{-1}(-\sqrt{2})$ |
(II) $\frac{3\pi}{4}$ |
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)