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

`<=>1 + \sin x + \sqrt{3} \cos x = 2`

 `<=>\sin x + \sqrt{3} \cos x = 1`

`<=>2 \sin(x + \frac{\pi}{3}) = 1`

`<=> \sin(x + \frac{\pi}{3}) = \frac{1}{2}`

`->x + \frac{\pi}{3} = \frac{\pi}{6} + k2\pi\text{hoặc}  \frac{5\pi}{6} + k2\pi`

`->x = -\frac{\pi}{6} + k2\pi  \text{hoặc} \frac{\pi}{2} + k2\pi`

Vậy `S={ -\frac{\pi}{6} + k2\pi  ; x = \frac{\pi}{2} + k2\pi | k \in ZZ}`