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Question
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Solution
Taking (n + 1)θ = A and (n – 1)θ = B
L.H.S = sin A sin B + cos A cos B
= cos(A – B)
= cos[(n + 1) – (n – 1)]θ
= cos(n + 1 – n + 1)θ
= cos 2θ
= R.H.S
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