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      Question

      If sin x + sin y = a and cos x + cos y = b, find sin(x +

      y):
      A a² - b² Correct Answer Incorrect Answer
      B a² + b² - 1 Correct Answer Incorrect Answer
      C 2ab Correct Answer Incorrect Answer
      D (a² + b²) / 2 Correct Answer Incorrect Answer

      Solution

      Using sum-to-product identities: sin x + sin y = 2sin((x + y)/2)cos((x - y)/2), cos x + cos y = 2cos((x + y)/2)cos((x - y)/2). Dividing and simplifying, we get: sin(x + y) = a² + b² - 1. Correct option: b

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