A

Given the position of a particle moving along the X-axis is described by the equation:
x = \sqrt{3} \sin(\omega t) - \cos(\omega t)
To find the region in which the particle is confined, we can analyze the range of this expression.
Step 1: Rewrite the equation in a suitable form by using the trigonometric identity A \sin(\theta) + B \cos(\theta) = R \sin(\theta + \phi), where R = \sqrt{A^2 + B^2} and the angles are appropriately calculated. Here, A = \sqrt{3} and B = -1.
Step 2: Calculate R:
R = \sqrt{(\sqrt{3})^2 + (-1)^2} = \sqrt{3 + 1} = \sqrt{4} = 2
Step 3: Find the range of R \sin(\theta + \phi):
The maximum and minimum values of 2 \sin(\omega t + \phi) will be 2 and -2 respectively.
Hence, the range of x is:
-2 \leq x \leq 2
Therefore, the particle is confined within the region x = [-2, 2].
Therefore, A.