If ^ -1 x=y, then - Vidyadip

MCQ

If $\tan ^{-1} x=y$, then

A
-1 < y<1
B
$\frac{-\pi}{2} \leq y \leq \frac{\pi}{2}$
C
$\frac{-\pi}{2}$ < y < $\frac{\pi}{2}$
D
$y \in\left\{\frac{-\pi}{2}, \frac{\pi}{2}\right\}$

✓

Answer

Range of $\tan ^{-1} x=\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$

$\therefore \frac{-\pi}{2}$< y < $\frac{\pi}{2}$

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