Answer :

Given,


cos (α + β) sin (γ + δ) = cos (α - β) sin (γ – δ)



Adding 1 both sides:





Now,



Subtracting 1 both sides:





Dividing equation (i) by equation (ii):










{sin (-A) = -sin A & cos (-A) = cos A}




cot α cot β cot γ = cot δ


Hence Proved


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