cos2x + cosx + sinx = 0.
<=>(cos^2x -sin^2x) + cosx + sinx = 0
<=>(cosx + sinx)(cosx -sinx+1) = 0
(cosx + sinx)=0 ; x=-pi/4 +kpi
(cosx -sinx+1) = 0
<=>(2cos^2 (x/2) -2sin(x/2).cos(x/2) =0
<=>cos (x/2) .(cos (x/2)-sin (x/2)) =0
cos (x/2) =0 => x/2 =pi/2 +kpi ; x = pi +2kpi
(cos (x/2)-sin (x/2))=0=> x/2 =pi/4 +kpi ; x=pi/2 +2kpi