若△ABC中,2√2(sin^2A-sin^2C)=(a-b)sinB外接圆半径为√21求角C2求面积最大值

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若△ABC中,2√2(sin^2A-sin^2C)=(a-b)sinB外接圆半径为√21求角C2求面积最大值若△ABC中,2√2(sin^2A-sin^2C)=(a-b)sinB外接圆半径为√21求角

若△ABC中,2√2(sin^2A-sin^2C)=(a-b)sinB外接圆半径为√21求角C2求面积最大值
若△ABC中,2√2(sin^2A-sin^2C)=(a-b)sinB外接圆半径为√2
1求角C
2求面积最大值

若△ABC中,2√2(sin^2A-sin^2C)=(a-b)sinB外接圆半径为√21求角C2求面积最大值
由正弦定理a/sinA=b/sinB=c/sinC=2R可将2√2(sin^2A-sin^2C)=(a-b)sinB转化为2√2[(a/2R)^2-(c/2R)^2]=(a-b)b/2R,整理得a^2+b^2-c^2=ab
∴cosC=(a^2+b^2-c^2)/2ab=1/2 ∴∠C为60° ∴∠A+∠B=120°
S=1/2absinC=4sinAsinB(根据正弦定理)
∠A=120°-∠B,代入化简求最值就行了