Question

If
x= sint,
y = cos2t then
prove that dy/dx= -4sint​

Answer 1

Step-by-step explanation:

Given,

$x = \sin(t) \: \: and \: \: y = \cos(2t)$

Now,

$\frac{dx}{dt} = \cos(t) \: \: and \: \: \frac{dy}{dt} = - 2 \sin(2t)$

So,

$= > \frac{dy}{dx} = \frac{ - 2 \sin(2t) }{ \cos(t) }$

$= > \frac{dy}{dx} = \frac{ - 4 \sin( t) \cos(t) }{ \cos(t) }$

$= > \frac{dy}{dx} = - 4 \sin(t)$