Mathematics - Trigonometric Equation Question with Solution | TestHub

Given equation is $${\sin }^{-1}x=2{\tan }^{-1}x$$ Now, this equation has only one solution. $$\begin{array}{rl}& \therefore \text{ LHS }={\sin }^{-1}1=\frac{\pi }{2}\\ & \text{ and }\text{ RHS }=2{\tan }^{-1}1=2\times \frac{\pi }{4}=\frac{\pi }{2}\end{array}$$ Also, $x=1$ gives angle value as $\frac{\pi }{4}$ and $\frac{5\pi }{4}$ $\frac{5\pi }{4}$ is outside the principal value.