Use the product-to-sum formulas to rewrite the product as a sum or difference. sin 8𝜃 sin 2𝜃

Answer 1

You can derive this from the cos sum formula or just know it.

cos(8θ - 2θ) = cos(8θ)cos(2θ) + sin(8θ)sin(2θ)

cos(8θ + 2θ) = cos(8θ)cos(2θ) - sin(8θ)sin(2θ)

As 8θ - 2θ = 6θ and 8θ + 2θ = 10θ, subtracting the second equation from the first, we get

cos(6θ) - cos(10θ) = 2 sin(8θ)sin(2θ)

Then, sin(8θ)sin(2θ) = 1/2(cos(6θ) - cos(10θ)) or 1/2 cos(6θ) - 1/2 cos(10θ)