Question

已知sin(α+β)sin(α-β)=m,求cos^2α-cos^2β

Answer 1

已知sin(α+β)sin(α-β)=m,求cos^2α-cos^2β
解答：sin(α+β)sin(α-β)=m=sin^2α-sin^2β
cos^2α-cos^2β=(1-sin^2α)-(1-sin^2β)=sin^2α-sin^2β=m

感谢网友批评指正 弄错了一个符号嘿嘿 回答了几十个问题 眼花了~~
修正解答：sin(α+β)sin(α-β)=m=sin^2α-sin^2β
cos^2α-cos^2β=(1-sin^2α)-(1-sin^2β)=-sin^2α+sin^2β=-m

补充：sin(α+β)sin(α-β)=(sinacosb+cosasinb)(sinacosb-cosasinb)
=(sinacosb)^2-(cosasinb)^2=sin^2α-sin^2β

Answer 2

根据公式：cosθ-cosφ=-2sin(θ/2+φ/2)sin(θ/2-φ/2)，cos^2α-cos^2β =1/2(cos2α-cos2β)=-m ，楼上的共识都错了，汗