Solution: tana/tanb = [(√ 2) c-b]/b = [(√ 2) sinc-sinb]/sinb = [(√ 2) sin (a+b)-sinb]/sinb.
Sina cosb/cosa sinB =[(√2)sin(A+B)-sinB]/sinB
Sina cosb =(√2)sin(A+B)cosA-sinb cosA
Sina cosb+cosA sinb =(√2)sin(A+B)cosA
sin(A+B)=(√2)sin(A+B)cosA
Therefore, cosA=(√2)/2, ∴A=π/4.