Answer
$\frac{\pi }{6}$ 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 $\cos \frac{\pi }{6}$ is given as $\frac{\sqrt{3}}{2}$, and $\sin \frac{\pi }{6}$ is given as $\frac{1}{2}$.
$\begin{align}
& \cos x+2=\sqrt{3}\sin x \\
& \cos \frac{\pi }{6}+2=\sqrt{3}\sin \frac{\pi }{6} \\
& \frac{\sqrt{3}}{2}+2=\sqrt{3}.\frac{1}{2} \\
& \frac{\sqrt{3}+4}{2}=\frac{\sqrt{3}}{2}
\end{align}$
Thus, $\cos x+2=\sqrt{3}\sin x$ is false.
