Range of coses^ -1 X is - Vidyadip

Question

Range of $\operatorname{coses}^{-1} X$ is

✓

Answer

$Y=\operatorname{coses}^{-1}(x)$ 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 $y=\operatorname{coses}$ $1( x )$(b) $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-\{0\}$
Explanation: To Find: The range of $\operatorname{coses}^{-1}( x )$
Here, the inverse function is given by $y=f^{-1}(x)$
The graph of the function $\operatorname{coses}^{-1}(x)$ can be obtained from the graph of
Below is the Graph of the range of $\operatorname{coses}^{-1}(x)$

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

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