在三角形ABC中，求证a²-b²/c²=sin(A-B)/sinC
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a/sinA=b/sinB=c/sinC
sin(A+B)=sinC
(sin^2A-sin^2B)/sin^2C=(sinA+sinB)(sinA-sinB)/sin^2C=2sin(A+B)/2*cos(A-B)/2*2cos(A+B)/2sin(A-B)/2 /sin^2C=sin(A+B)sin(A-B)/sin^2C=sin(A-B)/sinC
sin(A+B)=sinC
(sin^2A-sin^2B)/sin^2C=(sinA+sinB)(sinA-sinB)/sin^2C=2sin(A+B)/2*cos(A-B)/2*2cos(A+B)/2sin(A-B)/2 /sin^2C=sin(A+B)sin(A-B)/sin^2C=sin(A-B)/sinC
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