用弦化邊來做
∵2R(sin^2A-sin^2c)=(根號3*a-b)sinB
asinA-csinC=(根號3*a-b)sinB
a²-c²=根號3*ab-b²
∴cosC=(a²+b²-c²)/2ab=根號3*ab/2ab=根號3/2
C=π/6
S△abc=absinC/2=根號3ab/4≤根號3(a²+b²)/8,當且僅當a=b時等號成立.
此時,A=7π/12
由正弦定理,得
a/sinA=c/sinC=2R
a/sin(7π/12)=2R
a=(根號2+根號6）R
S△abc最大值=根號3a²/4=（2*根號3+3）R²