Find the value of dy/dx if $$x=cost,y=sint$$​.

Correct option is D

​$$\begin{aligned}&\text{We are given parametric equations:} \\&\quad x = \cos t \\&\quad y = \sin t \\&\text{We are to find:} \quad \frac{dy}{dx} \\\\&{{\text{Use Parametric Derivative Rule:}}} \\&\quad \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} \\\\&\text{Step-by-Step:} \\&\quad \frac{dy}{dt} = \frac{d}{dt}(\sin t) = \cos t \\&\quad \frac{dx}{dt} = \frac{d}{dt}(\cos t) = -\sin t \\\\&\text{So,} \quad \frac{dy}{dx} = \frac{\cos t}{-\sin t} = -\cot t\end{aligned}$$​​