If cos (α + β) sin (γ + δ) = cos (α - β) sin (γ - δ), prove that cot α cot β cot γ = cot δ

Question

Philoid · Accepted 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