A curve has the parametric equations
x=sec2t,y=2tant,0<t<π2 x = \sec^2 t, \quad y = 2\tan t, \quad 0 < t < \frac{\pi}{2} x=sec2t,y=2tant,0<t<2πFind an expression for dydx\displaystyle \frac{dy}{dx}dxdy in terms of ttt.
Find an equation of the tangent to the curve when t=π3\displaystyle t = \frac{\pi}{3}t=3π.
Find a cartesian equation for the curve.
