The point on the curve $y=\cos x-1, x \in\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]$ at which tangent is parallel to the x-axis is:

$(\pi,-2)$ $(-2, \pi)$ $(-\pi, 2)$ $(2,-\pi)$

$(\pi,-2)$

The correct answer is Option (1) → $(\pi,-2)$