Answer
For the provided equation, the value of x is $ x=\frac{\pi }{6},\frac{5\pi }{6},\frac{7\pi }{6},\frac{11\pi }{6}$.
Work Step by Step
We have the provided equation as $4{{\cos }^{2}}x=3$
Then, solving,
$\begin{align}
& 4{{\cos }^{2}}x=3 \\
& {{\cos }^{2}}x=\frac{3}{4} \\
& \cos x=\pm \frac{\sqrt{3}}{2}
\end{align}$
For $\cos x=\frac{\sqrt{3}}{2}$ in the given range,
$ x=\frac{\pi }{6},\frac{11\pi }{6}$
And for $\cos x=\frac{-\sqrt{3}}{2}$
$ x=\frac{5\pi }{6},\frac{7\pi }{6}$
Hence, we have $ x=\frac{\pi }{6},\frac{5\pi }{6},\frac{7\pi }{6},\frac{11\pi }{6}$.
