What is the value of the following expression?

$$\frac{\text{cos}\space \text{3x}+\text{cos}\space \text{x}}{\text{sin}\space \text{3x}-\text{sin}\space \text{x}}$$​

Correct option is D

Given:
​$$\frac{\cos 3x + \cos x}{\sin 3x - \sin x}$$​
Concept Used:
​$$\cos A + \cos B = 2 \cos\left(\frac{A + B}{2}\right) \cos\left(\frac{A - B}{2}\right) \\\sin A - \sin B = 2 \cos\left(\frac{A + B}{2}\right) \sin\left(\frac{A - B}{2}\right)$$​​
Formula Used:
​$$\cos 3x + \cos x = 2 \cos\left(\frac{3x + x}{2}\right) \cos\left(\frac{3x - x}{2}\right) = 2 \cos(2x) \cos(x) \\\ \\\sin 3x - \sin x = 2 \cos\left(\frac{3x + x}{2}\right) \sin\left(\frac{3x - x}{2}\right) = 2 \cos(2x) \sin(x) \\\ \\\frac{\cos 3x + \cos x}{\sin 3x - \sin x} = \frac{2 \cos(2x) \cos(x)}{2 \cos(2x) \sin(x)} = \frac{\cos(x)}{\sin(x)} = \cot(x)$$​​