Parameters with trig functions

Question

I'm having difficulty eliminating the parameter in the equations: $x = (tan^2\theta)$, $y = sec\theta$. The only strategy I know of for tackling trig parameters is to use the identity [$sin^2(x) + cos^2(x) = 1$] before setting that equal to some expression of $x + y$, but tangent gives me $x = \frac{sin^2\theta}{cos^2\theta}$, and I have no idea how to eliminate the denominator to get part of the identity. Am I just going about this completely wrong?

Thank you!

Answer 1

Squaring $y = \sec \theta$

$y^2 = \sec^2 \theta$

We know that,

$\sec^2 \theta - \tan^2 \theta = 1$

So we have,

$y^2 - x = 1$

Other method to drive. As you said,

$\sin^2 \theta + \cos^2 \theta = 1$

Divide above equation by $\cos^2 \theta$

$\tan^2 \theta + 1 = \sec^2 \theta$

$x + 1 = y^2$

Answer 2

Use,

$$\sin^2(\theta)+\cos^2(\theta)=1$$

Dividing both sides by $\cos^2 (\theta)$ gives:

$$\tan ^2 (\theta)+1=\sec^2 (\theta)$$

This should be enough to conclude.

$$x+1=y^2$$