If `x=asec^3theta and y=atan^3theta, ` find `(dy)/(dx) ` at `theta=pi/3`

Explanation

`x= asec^2 theta`

`y = a tan^3 theta`

`dx/(d theta)= 3a^2 sec^2 theta d/(d theta) sec theta`

`= 3a^2 sec^2 theta sec theta tan theta`

`= 3asec^2 theta tan theta`

now,`dy/(dtheta) = 3atan^2 theta d/(d theta) (tan theta) = 3atan^2theta sec^2 theta`

so, `(dy)/(dx) = (dy)/(d theta) xx (d theta)/(dx) `

`= (3atan^2 theta sec^2theta)/(3asec^2 theta tan theta) `

...