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Q.
The number of solutions of the equation $\left|\tan ^{-1}\right| x||=\sqrt{\left(x^{2}+1\right)^{2}-4 x^{2}}$ is
Inverse Trigonometric Functions
Solution:
$\sqrt{\left(x^{2}+1\right)^{2}-4 x^{2}}=\sqrt{\left(x^{2}-1\right)^{2}}=\left|x^{2}-1\right|$
$\Rightarrow \left|\tan ^{-1}\right| x \|=\left|x^{2}-1\right|$
Draw the graphs of $y =\left|\tan ^{-1}\right| x \|$ and $y =\left| x ^{2}-1\right|$
From the graph, it is clear that equation has four roots.
