Ta có : \(\left(\sin\dfrac{x}{2}+\cos\dfrac{x}{2}\right)^2+\sqrt{3}\cos x=2\)
\(\Leftrightarrow\sin^2\dfrac{x}{2}+2\sin\dfrac{x}{2}.\cos\dfrac{x}{2}+\cos^2\dfrac{x}{2}+\sqrt{3}\cos x-2=0\)
\(\Leftrightarrow1+\sin x+\sqrt{3}\cos x-2=0\)
\(\Leftrightarrow\sin x+\sqrt{3}\cos x=1\)
\(\Leftrightarrow\sin x.\cos\dfrac{\pi}{3}+\cos x.\sin\dfrac{\pi}{3}=\sin\left(x+\dfrac{\pi}{3}\right)=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{3}=\dfrac{\pi}{6}+k2\pi\\x+\dfrac{\pi}{3}=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\) \(\left(K\in Z\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{6}+k2\pi\\x=\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\) \(\left(K\in Z\right)\)
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