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