Question
If sin(x + y) = 3/5 and cos(x - y) = 12/13, where x, y
∈ [0, π/2], find sin(2x) + sin(2y).Solution
Let sin(x + y) = 3/5, so cos(x + y) = 4/5 using sin²θ + cos²θ = 1. Let cos(x - y) = 12/13, so sin(x - y) = 5/13 using sin²θ + cos²θ = 1. Use the identity sin(2x) + sin(2y) = 2[sin(x + y)cos(x - y)] to find: sin(2x) + sin(2y) = 2 × (3/5) × (12/13) = 72/65. Correct answer: d
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