余弦定理
cosB=(a^2+c^2-b^2)/(2ac)=1/2
∴B=π/3
(1)sin^2(A+C)/2+cos2B
=sin^2(π/2-B/2)+cos2B
=cos^2(B/2)+cos2B
=cos^2(π/6)+cos2π/3
=3/4-1/2
=1/4
(2)
b=2
△ABC面积=1/2*ac*sinB=√3/4*ac
余弦定理
(a^2+c^2-b^2)/(2ac)=1/2
(a^2+c^2-4)/(2ac)=1/2
a^2+c^2=4+ac
∵a^2+c^2>=2ac
∴4+ac>=2ac
ac