(1)
f(x)=sin²ωx+√3sinωxsin(ωx+二分之∏)+2cos²ωx
=1/2(1-cos2wx)+√3/2sin2wx+1+cos2wx
=√3/2sin2wx+1/2cos2wx+1/2
=sin(2wx+π/6)+1/2
∵f(x)图象的相邻两对称轴间的距离为∏
∴f(x)的半周期T/2=π,T=2π
由2π/(2w)=2π得w=1/2
∴f(x)=sin(x+π/6)+1/2
(2)
∵bcosC=(3a-c)cosB
本剧正弦定理：
a=2RsinA,b=2RsinB,c=2RsinC
∴sinBcosC=(3sinA-sinC)cosB
∴3sinAcosB=sinBcosC+cosBsinC=sin(B+C)
∵sin(B+C)=sin(180º-A)=sinA>0
∴3sinAcosB=sinA
∴cosB=1/3 ,sinB=2√2/3
∴f(B)=sin(B+π/6)+1/2
=sinBcosπ/6+cosBsinπ/6+1/2
=2√2/3*√3/2+1/3*1/2+1/2
=(2+√6)/3