Question

在△ABC中，与sin(A-B)/sinC相等的式子是 A，(a^2+b^2)/c^2 B,(a^2-b^2)/c^2 C,(a-b)/c D,(a^2-b^2)/c

请附上过程

Answer 1

sin(A-B)/sinC=(sinAcosB-cosAsinB)/ sinC
= sinA/ sinC *cosB-cosA*sinB/ sinC
=a/c*cosB-b/c* cosA
=a/c*(a^2+c^2-b^2)/(2ac)- b/c*(b^2+c^2-a^2)/(2bc)
=(a^2+c^2-b^2)/(2c^2)- (b^2+c^2-a^2)/ (2c^2)
=(2a^2-2b^2)/(2c^2)
=(a^2-b^2)/(c^2)
选B.