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a/sinA=b/sinB=c/sinC=k
a=ksinA,b=ksinB,c=ksinC
a²-b²/c²
=(sin^2A-sin^2B)/sin^2C
=(sinA+sinB)(sinA-sinB)/sin^2C
=2sin[(A+B)/2]cos[(A-B)/2]*2cos[(A+B)/2]sin[(A-B)/2]/sin^2C
=sin(A+B)sin(A-B)/sin^2C
=sin(A-B)/sinC
a=ksinA,b=ksinB,c=ksinC
a²-b²/c²
=(sin^2A-sin^2B)/sin^2C
=(sinA+sinB)(sinA-sinB)/sin^2C
=2sin[(A+B)/2]cos[(A-B)/2]*2cos[(A+B)/2]sin[(A-B)/2]/sin^2C
=sin(A+B)sin(A-B)/sin^2C
=sin(A-B)/sinC
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