cosA+2cos[(B+C)/2]=cosA+2cos[(pi-A)/2]=cosA+2sin(A/2)
=-2(sin(A/2)-1/2)^2+3/2sin(A/2)=1/2 时取得最大值A=60°
S=bc/2*sinA=√3bc/4
1+bc=a^2+2bccosA=b^2+c^2>=2bc
bc