Question

已知三角形ABC的三个内角ABC的对边分别为abc

Answer 1

cosA+2cos[(B+C)/2]=cosA+2cos[(pi-A)/2]=cosA+2sin(A/2)=1-2sin(A/2)^2+2sin(A/2)

=-2(sin(A/2)-1/2)^2+3/2 sin(A/2)=1/2 时取得最大值 又因为A=2bc

bc