sin a=√2sinb,...(1)
tana=√3tanb...(2)
(1)÷（2）得cosa=√2cosb/√3...(3)
(1)²+（3）²得1=2sin²b+2cos²b/3=2(1-cos²b)+2cos²b/3
cos²b=3/4
cosb=±√3/2
b∈(0,π)
所以b=π/6,或b=5π/6
sin a=√2sinb=√2/2
a∈(-π/2,π/2)
所以a=π/4,代入（2）检验得b=5π/6为增根
总上,a=π/4,b=π/6