# How do you solve sin2x = sinx?

Aug 15, 2015

Think of the double angle formula for $\sin 2 x$

#### Explanation:

$\sin 2 x = \sin x$
$2 \sin x \cos x = \sin x$
$2 \sin x \cos x - \sin x = 0$
$\sin x \left(2 \cos x - 1\right) = 0$
Solution A: $\sin x = 0 \setminus R i g h t a r r o w x = k \pi , k \in \mathbb{Z}$
Solution B: $2 \cos x = 1 \setminus R i g h t a r r o w \cos x = \frac{1}{2} , x = \pm \frac{\pi}{3} + 2 k \pi = \frac{\pi}{3} \left(6 k \pm 1\right) , k \in \mathbb{Z}$
$\therefore x = k \pi$ or $x = \frac{\pi}{3} \left(6 k \pm 1\right) , k \in \mathbb{Z}$