过程如下:tanA/tanB=(2c-b)/b.
sinA*cosB/(cosA*sinB)=(2c-b)/前渗b,
[a*(a^2+c^2-b^2)/2ac]/[b*(b^2+c^2-a^2)/2bc]=(2c-b)/b,
(a^2+c^2-b^2)/(b^2+c^2-a^2)=(2c-b)/b,
bc=b^2+c^2-a^2,
cosA=(b^2+c^2-a^2)/2bc=bc/2bc=1/2=cos60,
所顷清以慧乎脊A=60度.
tanA/tanB
=sinAcosB/(cosAsinB)
=2c/b-1
=2sinC/sinB-1(正弦定山穗理)
sinAcosB/(cosAsinB)=2sinC/sinB-1
去好唯桐掉友坦分母:sinAcosB=2sinCcosA-cosAsinB
sinAcosB+cosAsinB=2sinCcosA
即sin(A+B)=2sinCcosA=sinC
cosA=1/2
A=60°