I need help solving this question. I’ didn't get how to do it.

cos(A-B)/cos(A+B) + cos(C+D)/cos(C-D) =0

or cos(A-B)/cos(A+B) = -cos(C+D)/cos(C-D) .

Applying componendo and dividendo.

{cos(A-B)+cos(A+B)}/{cos(A-B)-cos(A+B)} ={-cos(C+D)+cos(C-D)}/{-cos(c+D)-cos(C-D)}.

2cosA.cosB/2sinA.sinB=2sinC.sinD/(-2cosC.cosD

or cotA.cotB = -tanC.tanD

or 1/(tanA.tanB) = -tanC.tanD.

by crossmultiplecation.

1= -tanA.tanB.tanC.tanD

or tanA.tanB.tanC.tanD = -1 ,proved.