1、f(x)=|AB|*|BC|cos（2π/3）=-|AB|*|BC|/2,
根据正弦定理,
|BC|/sinx=|AC|/sin（2π/3）,
|BC|=2√3sinx/3,
|AB|/sin(π-2/3π-x)=|AC|/sin（π/3-x）,
|AB|=2√3sin（π/3-x）/3,
f(x)=-(2√3sinx)*2√3sin（π/3-x）/9
∴f(x)=-4sinxsin(π/3-x)/3.
2、f(x)=-4sinxsin(π/3-x)=2[cosπ/3-cos(2x-π/3)]/3
=2(1/2-cos(2x-π/3)]/3
当cos(2x-π/3）=-1时,函数值最大,f(x)(max)=1,
当cos(2x-π/3）=1时,函数值最小,f(x)(min)=-1/3,
故值域为[-1/3,1].