sin2x + 2 cos x = 0
2sinxcosx + 2cosx = 0 divide through by 2
sinxcosx + cosx = 0 factor
cosx (sinx + 1) = 0
So either
cosx = 0 and this happens at pi/2 + pi*n where n is an integer
Or
sin x + 1 = 0
sin x = - 1 and this happens at 3pi /2 + 2pi*n where n is an integer