(1) 2cosA/2+cos(B+C)=2cos(A/2)-cosA
=-2[cos(A/2)-1/2]^2+3/2
当cos(A/2)=1/2时,取得最大值
A/2=60° A=120° C=60°-B
(2) S=(1/2)bcsinA=(1/2)*2*c*(√3/2)=2√3
c=4
a^2=b^2+c^2-2bccosA=4+16-2*2*4*(-1/2)
=20+8=28
a=2√7
(3) 由正弦定理a/sinA=b/sinB=c/sinC=2/(√3/2)=4/√3
b=4sinB/√3 c=4sinC/√3
S=(1/2)*bcsinA=(√3/4)*bc=(4√3/3)sinBsin(60°-B)
=(2√3/3)[cos(60°-2B)-cos60°]
=(2√3/3)[cos(60°-2B)-1/2]
可见cos(60°-2B)=1时
Smax=√3/3
此时B=C=30°