Question

The number of value(s) of $x$ satisfying $\sin \left(\frac{1}{3}{\cos }^{-1}x\right)=1$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

Given : $\sin \left(\frac{1}{3}{\cos }^{-1}x\right)=1$
$0\le {\cos }^{-1}x\le \pi \Rightarrow 0\le \frac{{\cos }^{-1}x}{3}\le \frac{\pi }{3}\Rightarrow 0\le \sin \left(\frac{{\cos }^{-1}x}{3}\right)\le \frac{\sqrt{3}}{2}\therefore \sin \left(\frac{1}{3}{\cos }^{-1}x\right)<1$
Hence, the given equation has no solution.