To simplify the expression $\frac{1}{\cos \theta} \div \frac{1}{\sin \theta}$, we can follow these steps:

1. Rewrite the division as multiplication: $\frac{1}{\cos \theta} \div \frac{1}{\sin \theta} = \frac{1}{\cos \theta} \times \frac{\sin \theta}{1}$

2. Simplify the expression: $\frac{\sin \theta}{\cos \theta}$

3. Recognize the trigonometric identity: $\frac{\sin \theta}{\cos \theta} = \tan \theta$

So, the simplified expression is $\tan \theta$.

Would you like further details or have any questions?

Here are five related questions you might find interesting:

1. How do you simplify $\sin \theta \times \tan \theta$?
2. What is the result of $\frac{1}{\tan \theta}$?
3. How do you express $\cot \theta$ using sine and cosine?
4. What is the identity for $\sin^2 \theta + \cos^2 \theta$?
5. How do you simplify $\frac{\cos \theta}{\sin \theta} \times \tan \theta$?

Tip: Trigonometric identities like $\tan \theta = \frac{\sin \theta}{\cos \theta}$ are very useful for simplifying expressions and solving equations in trigonometry.