2sinx*cosx+\sqrt{3}-2cosx-\sqrt{3}sinx=0  

[latex]2sinx*cosx + \sqrt{3} - 2cosx - \sqrt{3}sinx = 0[/latex] [latex]\sqrt{3}(1-sinx) - 2cosx(1-sinx) = 0[/latex]  [latex](1-sinx)(\sqrt{3}-2cosx) = 0[/latex]  1-sinx = 0   или 2cosx = sqrt(3)  sinx=1 [latex]x = \frac{\pi}{2}+2\pi n, [/latex] n - целое [latex]cosx = \frac{\sqrt{3}}{2}[/latex]  [latex]x = \frac{\pi}{6}+2\pi n,[/latex] n - целое