Question

[sin(4x) + sin(2x)] / [cos(4x) + cos(2x)] = √(3)

Answer 1

$$\begin{array}{l} \frac{\sin(4x) + \sin(2x)}{\cos(4x) + \cos(2x)} = \sqrt{3} \\ \tan(3x) = \sqrt{3} \end{array}$$

Results:

$$x = \frac{1}{9} (3\pi n + \pi) \quad \text{and} \quad n \in \mathbb{Z}$$

Possible intermediate steps:

$$\tan(3x) = \sqrt{3}$$

Take the inverse tangent of both sides:

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

Divide both sides by 3:

$$x = \frac{\pi}{9}$$