sin(A-B)/sinC=(sinAcosB-COSAsinB)/sinC=(acosB-bcosA)/c
cosB=(a²+c²-b²)/2ac
cosA=(b²+c²-a²)/2bc
(acosB-bcosA)/c=(a^2-b^2)/c^2
∴(a^2-b^2)/c^2=sin(A-B)/sinC
sin(A-B)/sinC=(sinAcosB-COSAsinB)/sinC=(acosB-bcosA)/c
cosB=(a²+c²-b²)/2ac
cosA=(b²+c²-a²)/2bc
(acosB-bcosA)/c=(a^2-b^2)/c^2
∴(a^2-b^2)/c^2=sin(A-B)/sinC