Answer :

Given,


cos (A + B) sin (C – D) = cos (A – B) sin (C + D)



Adding 1 both sides:





Now,



Subtracting 1 both sides:





Dividing equation (i) by equation (ii):











-tan D = tan A tan B tan C


tan D = -tan A tan B tan C


tan A tan B tan C + tan D = 0


Hence Proved


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