Question

If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx x = sin t, y = cos 2t

Answer 1

Given, $\bf{x=sint\:,\:y=cos2t}$

$\bf{\underline{x=sint}}$
now differentiate x with respect to t
dx/dt = d(sint)/dt = cost ----(1)

$\bf{\underline{y=cos2t}}$
now, differentiate y with respect to t,
dy/dt = d(cos2t)/dt = -2sin2t
dy/dt = -2(2sint.cost) = -4sint.cost---(2)

dividing equations (2) by (1),
{dy/dt}/{dx/dt}= (-4sint.cost)/cost = -4sint
dy/dx = - 4sint

hence, answer is $\bf{\frac{dy}{dx}=-4sint}$