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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.
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