Find $\frac{dy}{dx}$, if $x = a \cos \theta, y = a \sin \theta$.

$-\cot \theta$

The correct answer is Option (4) → $-\cot \theta$ ##

Given that

$x = a \cos \theta, y = a \sin \theta$

Therefore $\frac{dx}{d\theta} = -a \sin \theta, \frac{dy}{d\theta} = a \cos \theta$

Hence $\frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} = \frac{a \cos \theta}{-a \sin \theta} = -\cot \theta$