How to simplify trigonometric equations? (See details below)

Question

Here is the question I'm stuck on: 

 

The motion of point P is given by the following equations: 

 x(t) = -2 sin (t) cos (t)

 y(t) = cos (2t) 

The path traced by point p is called curve K. 

Prove that for all points on curve K the following relationship holds: x² = (2-2y)y²

 

First I substituted x(t) for x and y(t) for y and tried to simplify. However, I keep getting lost and there are so many expressions, so I'm beginning to wonder if there is an easier approach or something I'm not seeing about this relationship? 

Also how do I prove the relationship holds true? Does that mean to simply have both sides equal to each other in terms of cos/sin etc.? Please help! Thanks! 

 

Answer 1

You may start by noting that x(t) = -sin(2t)