Question

tan(α+β)/2=1/2,求cos2αcos2β-cos^2(α-β)的值

Answer 1

tan(α+β)/2=1/2,tan(α+β)=2

cos2αcos2β-cos^2(α-β)=1/2[cos(2α+2β)+cos(2α-2β)]-[cos(2α-2β)-1]/2

=1/2cos(2α+2β)+1/2=cos^2(α+β) =cos^2(α+β)/[cos^2(α+β)+cos^2(α+β)+]

=1/[1+ tan^2(α+β)]=1/5