shuxue

求三角形形状

(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(...全部

  (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 。
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