Which of the following is the range of the principal value of $\sec ^{-1} x$.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) - $[0, \pi]-\left\{\frac{\pi}{2}\right\}$
$y=\sec^{-1}x.$
$\text{Principal value range of } \sec^{-1}x \text{ is defined so that sec }y \text{ is one–one}.$
$y\in[0,\pi],\;y\ne\frac{\pi}{2}.$
$\text{Correct option: }[0,\pi]-\left\{\frac{\pi}{2}\right\}.$