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

1.	If`x=asec^3theta and y=atan^3theta, ` find `(dy)/(dx) ` at `theta=pi/3`
Answer» `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) ` `= (tan theta)/(sec theta) = sin theta` at `theta = pi/3` ``= sin pi/3 = sqrt3/2 Answer

Discussion

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