# Solve the equation sin x + sin 2x = 0 , for 0°< x < 360°?

May 10, 2018

#### Explanation:

show below

$\sin x + \sin 2 x = 0$

$\sin x + \left[2 \cdot \sin x \cdot \cos x\right] = 0$

$\sin x \left[1 + 2 \cos x\right] = 0$

$\sin x = 0$

$x = 0 , x = 2 \pi \mathmr{and} x = \pi$

$1 + 2 \cos x = 0$

$2 \cos x = - 1$

$\cos x = - \frac{1}{2}$

$x = \frac{2 \pi}{3} \mathmr{and} x = \frac{4 \pi}{3}$

note that

$\sin 2 x = 2 \cdot \sin x \cdot \cos x$