Giải phương trình \({\rm{2sin}}x\left( {{\rm{1}} + {\rm{cos2}}x} \right) + \sin 2x = {\rm{1}} + {\rm{2}}\cos x\)
A.\(S = \left\{ {\frac{{2\pi }}{3} + k2\pi ,\,\,\frac{\pi }{4} + k\pi ,\,\,k \in \mathbb{Z}} \right\}\)
B.\(S = \left\{ { \pm \frac{{2\pi }}{3} + k2\pi ,\,\,\frac{\pi }{4} + k\pi ,\,\,k \in \mathbb{Z}} \right\}\)
C.\(S = \left\{ { \pm \frac{{2\pi }}{3} + k2\pi ,\,\,\frac{\pi }{4} + k2\pi ,\,\,k \in \mathbb{Z}} \right\}\)
D.\(S = \left\{ {\frac{{2\pi }}{3} + k2\pi ,\,\,\frac{\pi }{4} + k2\pi ,\,\,k \in \mathbb{Z}} \right\}\)