Giải phương trình: \({\left( {\sin \frac{x}{2} + \cos \frac{x}{2}} \right)^2} + \sqrt 3 \cos x = 2\).

\({\left( {\sin \frac{x}{2} + \cos \frac{x}{2}} \right)^2} + \sqrt 3 \cos x = 2\)

\( \Leftrightarrow 1 + 2\sin \frac{x}{2}.\cos \frac{x}{2} + \sqrt 3 \cos x = 2\)

\( \Leftrightarrow \sin x + \sqrt 3 \cos x = 1 \Leftrightarrow \frac{1}{2}\sin x + \frac{{\sqrt 3 }}{2}\cos x\)(chia cả 2 vế cho 2)

\( \Leftrightarrow \cos \left( {x - \frac{\pi }{6}} \right) = \frac{1}{2} = \cos \frac{\pi }{3}\)

\( \Leftrightarrow x - \frac{\pi }{6} = \frac{\pi }{3} + k\pi \Leftrightarrow x = \frac{\pi }{2} + k\pi \left( {k \in \mathbb{Z}} \right)\).