题目有误
sin(α+β)×sin(α+β)=m
估计是sin(α+β)×sin(α-β)=m
sin(α+β)×sin(α-β)=(sinacosb+cosasinb)(sinacosb-cosasinb)
=sin^2acos^2b-cos^2asin^2b
=(1-cos^2a)cos^2b-cos^2a(1-cos^2b)
=cos^2b-cos^2acos^2b-cos^2a+cos^2acos^2b
=cos^2b-cos^2a
=m
cosα平方-cosβ平方=-m
题目有误
sin(α+β)×sin(α+β)=m
估计是sin(α+β)×sin(α-β)=m
sin(α+β)×sin(α-β)=(sinacosb+cosasinb)(sinacosb-cosasinb)
=sin^2acos^2b-cos^2asin^2b
=(1-cos^2a)cos^2b-cos^2a(1-cos^2b)
=cos^2b-cos^2acos^2b-cos^2a+cos^2acos^2b
=cos^2b-cos^2a
=m
cosα平方-cosβ平方=-m