∵1+tanA/tanB=sinC/sinB
∴tanB+tanA=2tanB*sinC/sinB
∴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(A+B),∴sinC=2sinC*cosA,
∵sinC≠0
∴cosA=1/2＞0(∴A是锐角）
∴A=π/3