[tex]cos2x+\sqrt{3}sin2x+\sqrt{3}sinx-cosx=2[/tex]
[tex]\Leftrightarrow \frac{1}{2}cos2x+\frac{\sqrt{3}}{2}sin2x+\tfrac{\sqrt{3}}{2}sinx-\frac{1}{2}cosx=1[/tex]
[tex]\Leftrightarrow cos\frac{\pi }{3}cos2x+sin\frac{\pi }{3}sin2x+cos\frac{\pi }{6}sinx-sin\frac{\pi }{6}cosx=1[/tex]
[tex]\Leftrightarrow cos(2x-\frac{\pi }{3})+sin(x-\frac{\pi }{6})=1[/tex]
[tex]\Leftrightarrow cos\left \lfloor 2(x-\frac{\pi }{6}) \right \rfloor+sin(x-\frac{\pi }{6})=1[/tex]
[tex]\Leftrightarrow 1-2sin^{2}(x-\frac{\pi }{6})+sin(x-\frac{\pi }{6})=1[/tex]
[tex]\Leftrightarrow \begin{bmatrix} sin(x-\frac{\pi }{6})=0 & \\ sin(x-\frac{\pi }{6})=\frac{1}{2} & \end{bmatrix}[/tex]
Đến đây bạn giải tiếp nhé!