1, (b-c)sinA+(c-a)sinB+(a-b)sinC
=(b-c)\(\frac{a}{2}\)R+(c-a)\(\frac{b}{2}\)R+(a-b)\(\frac{c}{2}\)R(正弦定理より)
=0

2,a(bcosC-ccosB)
=ab(\(a^{2}\)+\(b^{2}\)-\(c^{2}\))/2ab-ac(\(a^{2}\)+\(c^{2}\)-\(b^{2}\))/2ac
=(\(a^{2}\)+\(b^{2}\)-\(c^{2}\))/2-(\(a^{2}\)+\(c^{2}\)-\(b^{2}\))/2
=\(b^{2}\)-\(c^{2}\)