How do you solve $sin (2 x) - sin (x) = 0$ $sin(2x) - sin(x) = 0$ ?

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Answer 1 · 2016-05-18T02:59:14

Use the double angle formula $sin 2 x = 2 sin x cos x$ $sin2x = 2sinxcosx$

$2 sin x cos x - sin x = 0$ $2sinxcosx -sinx = 0$

$sin x (2 cos x - 1) = 0$ $sinx(2cosx - 1) = 0$

$sin x = 0 or cos x = \frac{1}{2}$ $sinx = 0 or cosx = 1/2$

$0˚ , 180˚ or x = 60˚, 300˚$

Therefore, our solution set is ${x = 0˚, 60˚, 180˚, 300˚}$ .

Hopefully this helps!

How do you solve sin(2x) - sin(x) = 0sin(2x)−sin(x)=0sin(2x) - sin(x) = 0?