The number of solutions of the equation, $\sin ^{-1} x=2 \tan ^{-1} x$ (in principal values) is :
The number of solutions of the equation, $\sin ^{-1} x=2 \tan ^{-1} x$ (in principal values) is :
1
4
2
3
Solution
Given equation is
$
\sin ^{-1} x=2 \tan ^{-1} x
$
Now, this equation has only one solution.
$
\begin{aligned}
& \therefore \quad \text { LHS }=\sin ^{-1} 1=\frac{\pi}{2} \\
& \text { and } \text { RHS }=2 \tan ^{-1} 1=2 \times \frac{\pi}{4}=\frac{\pi}{2}
\end{aligned}
$
Also, $x=1$ gives angle value as $\frac{\pi}{4}$ and $\frac{5 \pi}{4}$ $\frac{5 \pi}{4}$ is outside the principal value