If $x=a\, sin^3t$ and $y=acos^3t,$ then $\frac{dy}{dx}$ is equal to

tan t -tan t cot t -cot t

-cot t

The correct answer is Option (4) → $-\cot t$ $x=a\sin^3t$ and $y=a\cos^3t$ $\frac{dx}{dt}=3a\sin^2t\cos t$ $\frac{dy}{dt}=-a\cos^2t\sin t$ so $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=-\cot t$