Question: Given the set of parametric equations:
$x = 2 \tan t$
$y = 2 \cos^2 t$
Eliminate the parameter $t$ and find the rectangular equation for the curve.
How would I go about solving this? I know that when the equations involve $\sin$ and $\cos$ I can simply square and add them to $1$ but I don't know of any comparable identity for $\tan$ and $\cos^2$.
Hint $\to$
Given (1)$\cos^2t$ +$\sin^2t$=1 , (2) $\tan t$ =$\frac{sint}{cost}$
x=2$\tan t$ =2$\frac{sint}{cost}$, $x^2$=4$\tan ^2t$=4$\frac{sin^2t}{cos^2t}$
with y=2$\cos^2t$ , you should be able to finish the rest from here.