小花qj
幼苗
共回答了20个问题采纳率:90% 举报
根据正弦定理
a/sinA=b/sinB=c/sinC=2R
2R(sin² A-sin² C)=(√2*a-b)*sinB
a^2-c^2=√2ab-b^2
∴cosC=(a^2+b^2-c^2)/2ab=√2/2
∴sinC=√(1-cos^2C)=√2/2
S=1/2*absinC
=√2R^2sinAsinB
=√2R^2/2[cos(A-B)-cos(A+B)]
=√2R^2/2[cos(A-B)+cosC]
=√2R^2/2[cos(A-B)+√2/2]
≤√2R^2/2(1+√2/2)
=(1+√2)*R^2/2
S最大=a^2sinC/2=(√2+1)R^2/2
1年前
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nuiskswvan
举报
=√2R^2sinAsinB
=√2R^2/2[cos(A-B)-cos(A+B)]
这步怎么算?
举报
小花qj
积化和差公式:
sinαsinβ=-1/2[cos(α+β)-cos(α-β)]
这里的角是A、B