Question

Number of solutions of the equation $\sin \left(\frac{1}{3}{\cos }^{-1}x\right)=1$ are

• A. only one
• B. no solution
• C. only three
• D. at least two

Answer 1

The correct option is B no solution

$\sin \left(\frac{1}{3}{\cos }^{-1}x\right)=1$
$\Rightarrow \frac{1}{3}{\cos }^{-1}x=\frac{\pi }{2}$
$\Rightarrow {\cos }^{-1}x=\frac{3\pi }{2}$
$\Rightarrow \exists$ no solution, as $xϵ[0,\pi ]$