Question

若sin^2β-sin^2α=m,则sin(α+β)sin(α-β)

Answer 1

sin^2β-sin^2α=m

所以（1-cos^2β)-（1-cos^2α)=m

得打cos^2α-cos^2β=m

所以cos^2α=m+cos^2β

sin^2α=sin^2β-m

sin(α+β)sin(α-β)=sin^2αcos^2β-cos^2αsin^2β=(sin^2β-m)cos^2β-(m+cos^2β)sin^2β=-m