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Q.
The set of values of x satisfying $\left|\sin ^{-1} x\right|<\left|\cos ^{-1} x\right|$, is
Inverse Trigonometric Functions
Solution:
We know that $0 \leq \cos ^{-1} \leq \pi$.
$\therefore \left|\cos ^{-1} x\right|=\cos ^{-1} x$
It is evident from the graphs of $y =\left|\sin ^{-1} x \right|$
and $y=\left|\cos ^{-1} x\right|$ that $\left|\sin ^{-1} x\right|<\left|\cos ^{-1} x\right|$
for all $x \in[-1,1 / \sqrt{2}]$
