f(x)=-sinx+cos(1/2x+45°)=cos(x+90°）+cos(1/2x+45°)=2cos²(1/2x+45°)+cos(1/2x+45°)-1令cos(1/2x+45°)=t∈【-1,1】y=2t²+t-1对称轴 t=-1/4所以 t=-1/4,最小值为-9/8t=1,最大值2