For $x \in[-1,1]$, the number of solutions of the equation $\sin ^{-1} x=2 an ^{-1} x$ is equal to

Question

For $x \in[-1,1]$, the number of solutions of the equation $\sin ^{-1} x=2 	an ^{-1} x$ is equal to

Professor PC Thomas Classes · Answer

Let $	an^{-1}x = 	heta \Rightarrow x = 	an	heta$. $\sin^{-1}(	an	heta) = 2	heta$ forces $x=0,1, -1$. Thus 3 solutions.