# How do you solve 4sinx=2sinx+sqrt3?

Sep 2, 2016

$x = {60}^{\circ}$

#### Explanation:

$4 \sin x = 2 \sin x + \sqrt{3}$
$2 \sin x = \sqrt{3}$
$\sin x = \frac{\sqrt{3}}{2}$

$x = {60}^{\circ}$

Sep 4, 2016

$x = \frac{\pi}{3}$

#### Explanation:

We have: $4 \sin \left(x\right) = 2 \sin \left(x\right) + \sqrt{3}$

Let's subtract $2 \sin \left(x\right)$ from both sides of the equation:

$\implies 2 \sin \left(x\right) = \sqrt{3}$

Then, we can divide both sides by $2$ to get:

$\implies \sin \left(x\right) = \frac{\sqrt{3}}{2}$

$\implies x = \frac{\pi}{3}$

Therefore, the solution to the equation is $x = \frac{\pi}{3}$.