# If cos (A + B) si

Given,

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

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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