Match List I with List II
| List I | List II |
| A. $\sin^{-1}x+]cos^{-1}x,x∈[-1,1]$ | I. $-\frac{π}{2}$ |
| B. $\tan^{-1}\sqrt{3}-\cot^{-1}(\sqrt{3})$ | II. $-\frac{π}{6}$ |
| C. $\cos^{-1}\left(\cos\frac{13π}{6}\right)$ | III. $\frac{π}{2}$ |
| D. $\sin^{-1}(-\frac{1}{2})$ | IV. $\frac{π}{6}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
(A) $\sin^{-1}x+]cos^{-1}x=\frac{π}{2}$
(B) B. $\tan^{-1}\sqrt{3}-\cot^{-1}(\sqrt{3})$
$\frac{π}{3}-π+\cot^{-1}\sqrt{3}$
$=\frac{π}{3}-π-\frac{π}{6}=-\frac{π}{2}$
(C) $\cos^{-1}\left(\cos\frac{13π}{6}\right)=\cos^{-1}\left(\cos\left(2π+\frac{π}{6}\right)\right)$
$=\cos^{-1}\cos\frac{π}{6}=\frac{π}{6}$
(D) $\sin^{-1}(-\frac{1}{2})=-\frac{π}{6}$