已知函数f(x)=sin(x+π/6)+sin(x-π/6)-2cos^2(x/2),x∈[0,π] 求化简函数f(x)的解析式,

f(x)=sin(x+π/6)+sin(x-π/6)-2cos^2(x/2)=2sinxcosπ/6-(1+cosx)=根号3sinx-cosx-1=2（sinx根号3/2-1/2cosx）-1=2sin（x-π/6）-1f(x)=2sin（x-π/6）-1x∈[0,π],x-π/6∈[-π/6,5/6π],当x=2/3π时,sinx-π/6=1,...