
Parametric Equation
Eliminate t in the following equations to determine the type of curve represented.
x = cos t , y= 1  cos 2t
I have so far managed to reduce the y=1cos2t equation to 0 ? ,by using the addition formula and subing in x,to get rid of t.........but the ans is y= 2(1x^2) ,1<x<1.

Remember that $\displaystyle \cos{2t} = 2\cos^2{t}  1$.
So $\displaystyle y = 1  \cos{2t}$
$\displaystyle = 1  (2\cos^2{t}  1)$
$\displaystyle = 1  2\cos^2{t} + 1$
$\displaystyle = 2  2\cos^2{t}$
$\displaystyle = 2  2x^2$.
I think you can see that this is a Quadratic, and since $\displaystyle x = \cos{t}$ and $\displaystyle 1 \leq \cos{t} \leq 1$ for all $\displaystyle t$, that means $\displaystyle 1 \leq x \leq 1$.
