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Q. Complete solution set of $\tan ^{2}\left(\sin ^{-1} x\right)>1$ is

Inverse Trigonometric Functions

Solution:

$\tan ^{2}\left(\sin ^{-1} x\right)>1$
$\Rightarrow \frac{\pi}{4}<\sin ^{-1} x<\frac{\pi}{2}$ or $-\frac{\pi}{2}<\sin ^{-1} x<-\frac{\pi}{4}$
$\Rightarrow x \in\left(\frac{1}{\sqrt{2}}, 1\right)$ or $x \in\left(-1,-\frac{1}{\sqrt{2}}\right)$
$\Rightarrow x \in\left(-1,-\frac{1}{\sqrt{2}}\right) \cup\left(\frac{1}{\sqrt{2}}, 1\right)$