cosx/(1+cos2x)<0 => cosx/(sin(^2)x+cos(^2)x+cos(^2)x-sin(^2)x)<0 => cosx/2cos(^2)x<0 => 1/2cosx<0 => cosx>1/2 => x€(-pi/3+2pi*k; pi/3+2pi*k), k€Z