Answer
$\frac{\pi }{3}$ is not the solution of the given equation.
Work Step by Step
We know that according to the ratio table of trigonometry, the value of $\cos \frac{\pi }{3}$ is given as $\frac{1}{2}$, and $\sin \frac{\pi }{3}$ is given as $\frac{\sqrt{3}}{2}$.
$\begin{align}
& \cos x=\sin 2x \\
& \cos \frac{\pi }{3}=\sin 2.\frac{\pi }{3} \\
& \frac{1}{2}=\frac{\sqrt{3}}{2}
\end{align}$
Thus, $\cos x=\sin 2x$ is false.
