f(x)=sin^2﹙x/2﹢π/12﹚﹢√3sin﹙x/2﹢π/12 )cos(x/2+π/12﹚﹣1/2

由于(sinα)^2=1-(cosα)^2,且sinαcosα=sin(2α)/2
所以f(x)=1-(cos(x/2-π/12))^2+√3sin(x+π/6)/2-1/2
由于(cosα)^2=(1+cos(2α))/2
所以f(x)=1/2-(1+cos(x-π/6))/2+√3sin(x+π/6)/2=√3sin(x+π/6)/2-cos(x+π/6)/2
由于sin(π/3)=√3/2,cos(π/3)=1/2
所以f(x)=sin(π/3)sin(x+π/6)-cos(π/3)cos(π/6)
由于cosαcosβ-sinαsinβ=cos(α+β)
所以f(x)=-cos(x+π/6+π/3)=-cos(x+π/2)
则f(B)=-cos(B+π/2)=√3/2,所以cos(B+π/2)=-√3/2
由于B为锐角,所以B+π/2∈(π/2,π),则B+π/2可确定为5π/6,从而B=5π/6-π/2=π/3
2sinA=sinC=sin(π-(A+B))=sin(A+B)=sinAcosB+sinBcosA=sinA*cos(π/3)+cosA*sin(π/3)
即2sinA=sinA/2+√3cosA/2,有3sinA=√3cosA
由于A为锐角,cosA≠0,所以3sinA/cosA=√3,即tanA=√3/3
由于A为锐角,则可确定A=π/6,从而C=π-A-B=π-π/6-π/3=π/2
所以A=π/6,B=π/3,C=π/2