在三角形ABC中,已知tanA/tanB=2c-b/b,求角A
问题描述:
在三角形ABC中,已知tanA/tanB=2c-b/b,求角A
答
tanA/tanB= sinAcosB/sinBcosA c=2RsinC b=2RsinB所以 2 x 2RsinC - 2RsinB / 2RsinB = 2sinC-sinB/sinB所以sinAcosB/sinBcosA = 2sinC-sinB/sinB化简得sinAcosB+cosAsinB=2sinCcosA 又 sinC=sin(180°- (A+B))=sin(...