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:

$(\pi,-2)$

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

if tangent is parallel to x axis

$⇒\frac{dy}{dx}=0$

$y=\cos x-1$

$⇒\frac{dy}{dx}=\sin x=0$

$⇒x=π$ as $x∈[\frac{π}{2},\frac{3π}{2}]$

so $y=\cos π-1⇒y=-2$

$x,y=π,-2$