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

来源：学生作业帮助网编辑：六六作业网时间：2024/12/25 21:26:15

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
√2=a/(2sinA)=b/(2sinB)=c/(2sinC)
sinA=a/(2√2)
sinB=b/(2√2)
sinC=c/(2√2)
sin^2A-sin^2C=(a^2-c^2)/8
2√2（sin^2A-sin^2C）=（a-b）sinB
2√2（a^2-c^2）/8=（a-b）b/(2√2)
a^2-c^2=(a-b)b=ab-b^2
c^2=a^2+b^2-ab*1
=a^2+b^2-2ab*cosC
∴2cosC=1
cosC=1/2
∠C=π/3
c=2√2sinC=√6
面积S=c^2sinAsinB/[2sin(A+B)]
=c^2sinAsinB/(2sinC)
=6sinAsinB/√3
=2√3[cos(A-B)-cos(A+B)]
=2√3[cos(A-B)+cosC]
=2√3[cos(A-B)+1/2]
A=B时,cos(A-B)=1,S最大=3√3

在三角形ABC中,sinA-sinB/sin(A B)=√2sinA-si在三角形ABC中,sinA-sinB/sin(A B)=√2sinA-sinC/sinA sinB.(1)求B,(2)若cosA=3/5,求sinC的值在△ABC中,若sin^2A-sin^2B-sin^2C=sinBsinC,则∠A= 在△ABC中若sin^2A+sin^2B=2sin^2C 则∠C为? △ABC中,若sin^2A-sin^2B+sin^2C=sinAsinC那么角B= 在三角形ABC中,sin^2A 在三角形abc中 sin^2 A 在三角形abc中若sin^2A+sin^2B小于sin^2C,则三角形ABC的形状? 在△ABC中,求证；sin^(A/2)+sin^(B/2)+sin^(C/2)=1-2sin(A/2)sin(B/2)sin(C/2）证明：三角形ABC中,若sin²A+sin²B+sin²C＜2,三角形ABC为钝角三角形 △ABC中,若sin∧2A=sin∧2B+sin∧2C,且sinA=2sinB*cosC,判断△ABC的形状在△ABC中,若bsinB=csinC,且sin^2A=sin^2B+sin^2C则△ABC的形状为? 在△ABC中,若sinA=2sinBcosC,sin²A=sin²B+sin²C,试判断△ABC的形状在△ABC中,若sinA=2sinBcosC且sin²A=sin²B+sin²C,试判断△ABC的形状在三角形ABC中,若sin^A=sin^B+sin^C,且sinA=2sinBcosC,试判断△ABC的形状在三角形ABC中,若sin^2A=sin^2B+sin^2C+sinBsinC,求A的值 ⊿ABC中,若sin^2A+sin^2B+cos^2C 在三角形ABC中,若sin(2π-A)=-√2sin(π-B),√3cosA 在三角形ABC中,若sin（2π＋A）＝√2sin（π－B）,求