The equation of tangent to the curve $x= a cos^3t, y =a\, sin^3t$ at t is :

$xsect + y \, cosec t=a$

The correct answer is option (1) → $x\sec t+y\,cosec\,t=a$

$x= a \cos^3t, y =a\sin^3t$

$\frac{dx}{dt}=-3\cos^2y\sin t$, $\frac{dy}{dt}=3a\sin^2t\cos t$

so $\frac{dy}{dx}=\frac{-\sin t}{\cos t}$

so eq. → $y-a\sin^3t=\frac{-\sin t}{\cos t}(x-a\cos^3t)$

$y\,cosec\,t-a\sin^2t=a\cos^2t-x\sec t$

$x\sec t+y\,cosec\,t=a$