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Question
Express the following as a sum or difference
2 sin 10θ cos 2θ
Solution
2 sin 10θ cos 2θ
We know
2 sin A cos B = sin(A + B) + sin(A – B)
Take A = 10θ, B = 2θ
2 sin 10θ . cos 2θ = sin(10θ + 2θ) + sin(10θ – 2θ)
2 sin 10θ . cos 2θ = sin 12 θ + sin 8θ
2 sin 10θ . cos 2θ = `1/2`[sin 12θ + sin 8θ]
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