To simplify the given trigonometric expression:

$\text{tan}^2 x - \text{sec}^2 x$

We can use the Pythagorean identity:

$\text{sec}^2 x = 1 + \text{tan}^2 x$

Substitute this identity into the original expression:

$\text{tan}^2 x - \text{sec}^2 x = \text{tan}^2 x - (1 + \text{tan}^2 x)$

Simplifying further:

$\text{tan}^2 x - 1 - \text{tan}^2 x = -1$

Thus, the simplified expression is:

$\boxed{-1}$

Would you like further details or have any questions?

Here are 5 related questions:

1. What are the other Pythagorean trigonometric identities?
2. How do you derive the identity $\sec^2 x = 1 + \tan^2 x$?
3. Can this expression have a real value if $x$ is undefined for secant?
4. How does the tangent and secant function relate geometrically on the unit circle?
5. What is the domain of $\sec(x)$ and $\tan(x)$?

Tip: When simplifying trigonometric expressions, always look for identities like Pythagorean or angle sum formulas to reduce complexity.