Question

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

Answer 1

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

$\sqrt{3}(1-sinx) - 2cosx(1-sinx) = 0$ 

$(1-sinx)(\sqrt{3}-2cosx) = 0$ 

1-sinx = 0   или 2cosx = sqrt(3)

 sinx=1

$x = \frac{\pi}{2}+2\pi n,$ n - целое

$cosx = \frac{\sqrt{3}}{2}$ 

$x = \frac{\pi}{6}+2\pi n,$ n - целое