A. The domain of $\sin ^{-1} x$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
B. The range of $cosec^{-1} x$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$
C. The domain of $\sec ^{-1} x$ is $[0, \pi]-\left\{\frac{\pi}{2}\right\}$
D. The range of $\cot ^{-1} x$ is $(0, \pi)$
E. The range of $\tan ^{-1} x$ is $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

Choose the correct answer from the options given below:

B, D, E only

The correct answer is Option (3) - B, D, E only

A. false, domain of $\sin^{-1}x$ is [-1, 1]

B. true

C. false, domain of $\sec^{-1}x$ is $R-(-1, 1)$

D. true

E. true