2asin(C+π/6) = b+c根据正弦定理有：2sinAsin(C+π/6) = sinB+sinC2sinA{sinCcosπ/6+cosCsinπ/6) = sinB+sinCsinA{√3sinC+cosC) = sinB+sinC√3sinAsinC+sinAcosC = sinB+sinC又，sinB=sin(A+C) = sinAcosC+cosAsinC∴ √3sinAsinC+sinAcosC = sinAcosC+cosAsinC +sinC∴ √3sinAsinC =cosAsinC +sinC两边同除以sinC得：√3sinA =cosA + 1√3sinA - cosA = 12(sinAcosπ/6 - cosAsinπ/6) = 1sin（A-π/6) = 1/2A-π/6 ≠ 5π/6∴ A-π/6 = π/6∴ A = π/3
