The expression you provided is:

$\frac{1 - \sin(\theta)}{\cos(\theta)}$

To simplify or further analyze this expression, let's look at it in its current form.

It doesn't simplify in a straightforward way with basic trigonometric identities, but it can be expressed in a different form for specific purposes, such as solving for $\theta$ or applying it in certain integrals or limits.

If you want to further analyze or simplify it, you could use specific identities depending on what you are trying to achieve (e.g., solving for $\theta$, simplifying for an integral, etc.).

Would you like to explore this expression further or see how it behaves in specific cases? Let me know!

Related Questions:

1. What is the equivalent form of $\frac{1 - \sin(\theta)}{\cos(\theta)}$ using the identity $\sin^2(\theta) + \cos^2(\theta) = 1$?
2. How does this expression behave when $\theta = 0$ or $\theta = \pi/2$?
3. How would you integrate the expression $\frac{1 - \sin(\theta)}{\cos(\theta)}$?
4. What happens to the expression if $\theta$ approaches values where $\cos(\theta)$ is 0, such as $\theta = \frac{\pi}{2}$?
5. Can this expression be rewritten in terms of tangent using the identity $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$?

Tip:

If you ever encounter a complex trigonometric expression, check if there are known identities like $\sin^2(\theta) + \cos^2(\theta) = 1$ or the double angle formulas to simplify it.