已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2

已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2
已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2

已知αβ为锐角,且3sin^2 α+2sin^2β=1,3sin2α-2sin2β=0,求证α+2β=π/2
3sin^2α=cos2β 6cosαsinα=2sin2β
所以3sin^2α*2sin2β=6cosαsinαcos2β sinαsin2β=cosαcos2β
所以cos(2β+α)=0 又2β+α∈(0,3π/2) 所以α+2β=π/2