b=c,2sinB=根3sinA
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2R(sinA+sinC)(sinA-sinC)=(√3a-b)sinB有正弦定理2RsinA=a,2RsinC=c所以(a+c)(sinA-sinC)=(√3a-b)sinBsinA=a/2R,si
要证3sinB=sin(2A+B)即证3sin(A+B-A)=sin(A+B+A)即证3sin(A+B)cosA-3cos(A+B)sinA=sin(A+B)cosA+cos(A+B)sinA即证2s
5sinB=sin(2A+B)=sin(A+B+A)=sin(A+B)cosA+cos(A+B)sinA,sinB=sin(A+B-A)=sin(A+B)cosA-cos(A+B)sinA5sin(A
sina+cosb=1/3,平方sin^2a+2sinacosb+cos^2b=1/9sinb-cosa=1/2,平方sin^2b-2cosasinb+cos^2a=1/4相加2-2(sinacosb
a²-b²=√3bcsinC=2√3sinB→2R*sinC=2R*2√3sinB→c=2√3b→c²=2√3bccosA=(b²+c²-a²
应当是sin^2A+sin^2B【+】sin^2C=sinB*sinC+sinC*sinA+sinA*sinB吧括号中是要改的.两边同乘以22sin²A+2sin²B+2sin&s
3sinb=sin(2a+b)可得sin(2a+b)-sinb=2sinb由两角正弦差的公式:sin(2a+b)-sinb=2cos[(2a+b+b)/2]sin[(2a+b-b)/2]=2cos(a
打开平方得:sin^2A+sin^2B-sin^C=sinA*sinB正弦定理sinA=a/2R其它也一样a2/4R2+b2/4R2-c2/4R2=ab/4R2a2+b2-c2=ab余弦定理a2+b2
sinb=sin[(a+b)-a]=sin(a+b)cosa-cos(a+b)sina=sin(a+b)cosa-sinb/sina*sina=sin(a+b)cosa-sinb2sinb=sin(a
左边=sin(A+B)sin(B-A)+sin²C=sin(180-C)sin(B-A)+sin²C=sinCsin(B-A)+sin²C=sinC[sin(B-A)+s
左边=sin(A+B)sin(B-A)+sin²C=sin(180-C)sin(B-A)+sin²C=sinCsin(B-A)+sin²C=sinC[sin(B-A)+s
用三角形的面积公式s=(a*b*SinC)/2(正弦定理得到)现在,角c知道了.只要求a*b的最大值.正弦定理:a/sina=b/sinb=c/sinc=外接圆的直径=4(画圆可证明)所以a*b==4
2R(sinA+sinC)(sinA-sinC)=(√3a-b)sinB有正弦定理2RsinA=a,2RsinC=c所以(a+c)(sinA-sinC)=(√3a-b)sinBsinA=a/2R,si
1)sin(B+C)=sinA=2sinBsinA/sinB=2=a/ba=2b=2根52)cos(B+C)=-cosA=-(b^2+c^2-a^2)/2bc=根5/5
a/sinA=b/sinB=c/sinC=2R=2√2=>a=2RsinA,b=2RsinB,c=2RsinC2√2(sin²A-sin²C)=(a-b)sinB=>4R²
三角形三角必须满足关系a/sinA=b/sinB=c/sinC.
sin²A-sin²B-sin²C=sinBsinCa/sinA=b/sinB=c/sinC则由sin²A-sin²B-sin²C=sinB
因为m垂直n所以m×n=0(要加向量符号)即(sinB+sinC,sinA-sinB)×(sinB-sinC,sin(B+C))=0又sin(B+C)=sin(π-A)=sinA所以原式=[(sinB
这里要用到三角函数中和差化积的公式:sinA-sinB=2cos[(A+B)/2]sin[(A-B)/2]=2sin(C/2)sin[(A-B)/2]sinA+sinB=2sin[(A+B)/2]co