已知(cosA+2cosC)/(cosA+2cosB)=(sinB/sinC)求三角形ABC形状
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已知(cosA+2cosC)/(cosA+2cosB)=(sinB/sinC)求三角形ABC形状
已知(cosA+2cosC)/(cosA+2cosB)=(sinB/sinC)求三角形ABC形状
已知(cosA+2cosC)/(cosA+2cosB)=(sinB/sinC)求三角形ABC形状
(cosA+2cosC)/(cosA+2cosB)=sinB/sinC
cosAsinC+2sinCcosC=cosAsinB+2sinBcosB
cosAsinC+sin2C=cosAsinB+sin2B
cosAsinC-cosAsinB=sin2B-sin2C
cosA(sinC-sinB)=2cos(B+C)sin(B-C)
cosA(sinC-sinB)=2cos(180-A)sin(B-C)
cosA(sinC-sinB)=2cosAsin(C-B)
cosA[sinC-sinB-2sin(C-B)]=0
cosA=0,A=90度,直角三角形
或
sinC-sinB-2sin(C-B)=0
2cos[(C+B)/2]sin[(C-B)/2]-4sin[(C-B)/2]cos[(C-B)/2]=0
sin[(C-B)/2]{cos[(C+B)/2]-2cos[(C-B)/2]}=0
sin[(C-B)/2]=0,C=B,等腰三角形
或
cos[(C+B)/2]=2cos[(C-B)/2]>0
cos在0度-90度是减函数,显然不成立,舍去
所以是直角三角形 或等腰三角形
这类问题主要是注意转化!~~希望下面答案帮到你(cosA+2cosC)/(cosA+2cosB)=sinB/sinC
cosAsinC+2sinCcosC=cosAsinB+2sinBcosB
cosAsinC+sin2C=cosAsinB+sin2B
cosAsinC-cosAsinB=sin2B-sin2C
cosA(sinC-sinB)=2cos(B+C)si...
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这类问题主要是注意转化!~~希望下面答案帮到你(cosA+2cosC)/(cosA+2cosB)=sinB/sinC
cosAsinC+2sinCcosC=cosAsinB+2sinBcosB
cosAsinC+sin2C=cosAsinB+sin2B
cosAsinC-cosAsinB=sin2B-sin2C
cosA(sinC-sinB)=2cos(B+C)sin(B-C)
cosA(sinC-sinB)=2cos(180-A)sin(B-C)
cosA(sinC-sinB)=2cosAsin(C-B)
cosA[sinC-sinB-2sin(C-B)]=0
cosA=0,A=90度,直角三角形
或
sinC-sinB-2sin(C-B)=0
2cos[(C+B)/2]sin[(C-B)/2]-4sin[(C-B)/2]cos[(C-B)/2]=0
sin[(C-B)/2]{cos[(C+B)/2]-2cos[(C-B)/2]}=0
sin[(C-B)/2]=0,C=B,等腰三角形
或
cos[(C+B)/2]=2cos[(C-B)/2]>0
cos在0度-90度是减函数,显然不成立,舍去
收起
(cosA+2cosC)/(cosA+2cosB)=sinB/sinC
cosAsinC+2sinCcosC=cosAsinB+2sinBcosB
cosAsinC+sin2C=cosAsinB+sin2B
cosAsinC-cosAsinB=sin2B-sin2C
cosA(sinC-sinB)=2cos(B+C)sin(B-C)
cosA(si...
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(cosA+2cosC)/(cosA+2cosB)=sinB/sinC
cosAsinC+2sinCcosC=cosAsinB+2sinBcosB
cosAsinC+sin2C=cosAsinB+sin2B
cosAsinC-cosAsinB=sin2B-sin2C
cosA(sinC-sinB)=2cos(B+C)sin(B-C)
cosA(sinC-sinB)=2cos(180-A)sin(B-C)
cosA(sinC-sinB)=2cosAsin(C-B)
cosA[sinC-sinB-2sin(C-B)]=0
cosA=0,A=90度,直角三角形
或
sinC-sinB-2sin(C-B)=0
2cos[(C+B)/2]sin[(C-B)/2]-4sin[(C-B)/2]cos[(C-B)/2]=0
sin[(C-B)/2]{cos[(C+B)/2]-2cos[(C-B)/2]}=0
sin[(C-B)/2]=0,C=B,等腰三角形
或
cos[(C+B)/2]=2cos[(C-B)/2]>0
cos在0度-90度是减函数,显然不成立,舍去
收起