Question

已知sin(α+β)sin(β-α)=m,求cos^2α-cos^2β

Answer 1

由结论sin(α＋β)·sin(α－β)=sin^2α－sin^2β可得.

∵ sin(α＋β)·sin(β－α)=sin^2β－sin^2α

而 sin^2β－sin^2α=1－cos^2β－1＋cos^2α=cos^2α－cos^2β.

∴ cos^2α－cos^2β=sin(α＋β)·sin(β－α)=m.