由1+tanA/tanB=2c/b得,
tanB+tanA=2tanB*c/b,由正弦定理得c/b=sinC/sinB,故得
tanB+tanA=2tanB*sinC/sinB=2sinC/cosB
即tanB+tanA=2sinC/cosB
sinB*cosA+sinA*cosB=2sinC*cosA
sin(A+B)=2sinC*cosA,
sinC=sin(180°-A-B)=sin(A+B)=2sinC*cosA,sinC=2sinC*cosA,
由sinC不等于零,故得cosA=1/2,A=30°,