√3 sin2x+ 2 cos²x=2
↔√3 sin 2x+ 2 $\frac{1+ cos 2x}{2}$ =2
↔√3 sin2x + cos2x=1
↔$\frac{√3}{2}$ sin2x + $\frac{1}{2}$ cos2x= $\frac{1}{2}$
↔sin (2x+ π /6)= sin π/6
↔ \(\left[ \begin{array}{l}2x+π/6= π/6+ k2π\\2x+ π/6= π- π/6 +k2π\end{array} \right.\)
↔\(\left[ \begin{array}{l}x=kπ\\x=π/3 +kπ\end{array} \right.\)