Mark the tick against the correct answer in the following: Range of \operatorname{coses}^{-1} \mathrm{x} is
A. \left(\frac{-\pi}{2}, \frac{\pi}{2}\right)
B. \left[\frac{-\pi}{2}, \frac{\pi}{2}\right]
C. \left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-\{0\}
D. None of these
Mark the tick against the correct answer in the following: Range of \operatorname{coses}^{-1} \mathrm{x} is
A. \left(\frac{-\pi}{2}, \frac{\pi}{2}\right)
B. \left[\frac{-\pi}{2}, \frac{\pi}{2}\right]
C. \left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-\{0\}
D. None of these

Solution:

Option(C) is correct.
To Find: The range of \operatorname{cosec}^{-1}(x)
Here,the inverse function is given by \mathrm{y}=\mathrm{f}^{-1}(x)
The graph of the function y=\operatorname{cosec}^{-1}(x) can be obtained from the graph of Y=\operatorname{cosec} x by interchanging x and y axes.i.e, if (a, b) is a point on Y=\operatorname{cosec} x then (b, a) is the point on the function y=\operatorname{cosec}^{-1}(x)
Below is the Graph of the range of \operatorname{cosec}^{-1}(x)


From the graph it is clear that the range of \operatorname{cosec}^{-1}(x) is restricted to interval
\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}