余弦定理怎么证明？

1,AB+BC=AC(全是向量)
两边平方展开就能得到余弦定理了
2,利用正弦定理
AB^2+AC^2-2AB*ACcosA
=4R^2[(sinC)^2+(sinB)^2-2sinCsinBcosA]
=4R^2[(sinC)^2+(sinB)^2-2sinCsinB(-cos(B+C))]
=4R^2[(sinC)^2+(sinB)^2-2sinCsinB(-cosBcosC+sinBsinC)]
=4R^2[(sinC)^2+(sinB)^2+2sinBsinCcosBcosC-2(sinCsinB)^2]
=4R^2[(sinCcosB)^2+(sinBcosC)^2+2sinBsinCcosBcosC]
=4R^2(sinCcosB+sinBcosC)^2
=4R^2(sinA)^2
=BC^2