$\begin{array}{l}
{\left( {{{\sin }^2}\frac{x}{2} + {{\cos }^2}\frac{x}{2}} \right)^2} + \sqrt 3 \cos x = 2\\
\Leftrightarrow 1 + \sqrt 3 \cos x = 2\\
\Leftrightarrow \sqrt 3 \cos x = 1\\
\Leftrightarrow \cos x = \frac{1}{{\sqrt 3 }}\\
\Leftrightarrow x = \pm arc\,\,\cos \frac{1}{{\sqrt 3 }} + k2\pi
\end{array}$