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Match List I with List II
 List I List II
 A. The range of $\sin^{-1}x$ is
 I. $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]-{0}$
 B. The range of $\tan^{-1}x$ is
 II. $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$
 C. The range of $\csc^{-1}x$ is
 III. $[0,\pi] - \{\frac{\pi}{2}\}$
 D. The range of $\sec^{-1}x$ is

 IV. $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

Choose the correct answer from the options given below:





Solution

Range of $\sin^{-1}x$ is $[-\frac{\pi}{2},\frac{\pi}{2}]$ So A → IV Range of $\tan^{-1}x$ is $(-\frac{\pi}{2},\frac{\pi}{2})$ So B → II Range of $\csc^{-1}x$ is $[-\frac{\pi}{2},\frac{\pi}{2}] - {0}$ So C → I Range of $\sec^{-1}x$ is $[0,\pi] - {\frac{\pi}{2}}$ So D → III


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