已知sinα=根号2 cosβ,tanα=根号3 cotβ,-π/2

sinα=根号2 cosβ
cosβ=1/2根号2sinα
tanα=根号3 cotβ
sinα/ cosα=3 cosβ/sinβ
sinβ=1/2根号6cosα
sin^2β+cos^2β
=1
sin^2α+3cos^2α=2
又sin^2α+cos^2α=1
cos^2α=1/2
,
-π/2<α<π/2,0<β<π
sinβ=根号3/2,cosβ=1/2
所以α=π/4,β=π/3