The rectangular equation of the curve given parametrically by $x(t)=\tan (t)$ and $y(t)=\cos^2(t)$ is what?

Question

The rectangular equation of the curve given parametrically by $x(t)=\tan (t)$ and $y(t)=\cos^2(t)$ is what?

In a normal situation I would have set $t$ equal to something but in this case it becomes very messy

I had set $\arctan(x)=t$ and plugged that into the other to get $y(t)=\cos^2(\arctan(x))$

but that got me no where and I was wondering if there was any better way of doing this?

edit: new steps

So I have developed other methods which is listed below:

set $\cos(t)=\sqrt{y}$

and then we have $\frac{\sin(t)}{\sqrt{y}}=x$ but I still got no where

Answer 1

Note that $$\cos^2(t) = \frac{1}{\sec^2(t)} = \frac{1}{1 + \tan^2(t)}$$ so the equation is $y = 1/(1 + x^2)$