SOLUTION: What are the possible answers? sin(x) - sin(3x) = 0

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sin(x) - sin(3x) = 0
sin(x) = sin(3x)
are integers:



and




Answer: and

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This will take a while...please follow along...from
sin x - sin 3x = 0 we get
sin x - sin (x + 2x) = 0
sin x - (sin x cos 2x - sin 2x cos x) = 0
sin x - (sin x * (cos^2 x - sin^2 x) - 2 sin x cos * cos x) = 0
sin x - (sin x * (cos^2 x - sin^2 x) - 2 sin x cos^2 x) = 0
how factor out sin x
sin x(1 - cos^2 x + sin^2 + 2 cos^2 x) = 0
sin x(1 + cos^2 x + sin^2) = 0
2 sin x = 0
sin x = 0
x = 0, pi