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Two sine functions
Sin[a x] + Sin[b x] can be rewritten as 2 Sin[1/2(a + b) x] Cos[1/2(a - b) x] (using TrigFactor ), implying that the function has two families of equally spaced zeros: 2 π n/(a + b) and 2 π (n + 1/2)/(b - a) .