cos2x+sinx+a>=0
-1<=sinx=t<=1
2t^2-t-a-1<=0
2(t-1/4)^2<=9/8+a
因为：2(t-1/4)^2<=25/8,t=-1等号成立
所以9/8+a>=25/8
a>=2
a的范围a>=2