[latex]\sqrt{3}sin2x+cos2x+1=0, \left[\begin{array}{ccc}\pi\pi\\2\end{array}\right][/latex]

[latex]2\sqrt{3}sinxcosx +cos^2x-sin^2x+sin^2x+cos^2x=0\\ 2\sqrt{3}sinxcosx+2cos^2x = 0\\ cosx(\sqrt{3}sinx+cosx) = 0\\ cosx = 0\ \ \ \ \ \ \ \ \ \ \ \ \sqrt{3}sinx+cosx=0\ \ \ \ \ \ \ |:cosx\\ x = \pi+ \pi k \ \ \ \ \ \ \ \ \ \sqrt{3}tgx+1=0\\ .\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ tgx = -\frac{1}{\sqrt{3}}\\ .\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{5 \pi}{6} + \pi k[/latex]   я тут вспомнила, что недорешала вам) интервал [П/2;П] x = П и 5П/6