再三角形ABC中,角ABC所对的边分别为abc,求证：a的平方 -b的平方/c的平方=Sin（A+B）/SinC

根据正弦定理,a/sinA=b/sinB=c/sinC=2R
a^2=4R^2sin^2A
b^2=4R^2sin^2B
c^2=4R^2sin^2C
(a^2-b^2)/c^2=(sin^2A-sin^2B)/sin^2C=(sinA+sinB)(sinA-sinB)/sin^2C
=2sin(A+B)/2cos(A-B)/2*2cos(A+B)/2sin(A-B)/2
=sin(A+B)sin(A-B)/sin^2C
A+B=180-C
sin(A+B)=sin(180-C)=sinC
原式=sin（A-B）/sinC
你的结果是不是打错了?