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If $\sin ^{-1} x=y$, then
(a) $0 \leq y \leq \pi$
(b) $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
(c) $0 < y < \pi$
(d) $-\frac{\pi}{2} < y < \frac{\pi}{2}$
(a) $0 \leq y \leq \pi$
(b) $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
(c) $0 < y < \pi$
(d) $-\frac{\pi}{2} < y < \frac{\pi}{2}$
Solution:
1792 Upvotes
Verified Answer
The range of principal value of $\sin ^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
$\therefore$ if $\sin ^{-1} x=y$ then $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$ Option (b) is correct.
$\therefore$ if $\sin ^{-1} x=y$ then $-\frac{\pi}{2} \leq y \leq \frac{\pi}{2}$ Option (b) is correct.
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