What is the implicit form of $x=cos(t),y=-3+cos(2t)$?

Question

I know I have to use the properties of the trigonometric functions but I don't know which of them would help me get the answer.

Answer 1

$y + 3 = \cos (2t) = 2\cos^2t-1 = 2x^2-1\to y = 2x^2-4$. So if you want to find $\dfrac{dy}{dx}$ then from this $y' = 4x$

Answer 2

Hint: Use chain rule: $\frac{dy}{dx}=\frac{dy}{dt} \times \frac{dt}{dx}$. First find $\frac{dy}{dt}$ and $\frac{dx}{dt}$.