Question

已知sin(α+β)*sin(α-β)=-1/3,求sin^2α-sin^2β的值

Answer 1

sin(α+β)*sin(α-β)=(sinαcosβ)^2-(cosαsinβ)^2=-1/3

(1-sin^2β)sin^2α-(1-sin^2α)sin^2β=-1/3

sin^2α-sin^2βsin^2α-sin^2β+sin^2αsin^2β=-1/3

sin^2α-sin^2β=-1/3