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.

Understand how to simplify the trigonometric expression 1/cos ÷ 1/sin by using the identity \(\frac{\sin \theta}{\cos \theta} = \tan \theta\). This problem focuses on key trigonometric concepts and is suitable for students in Grades 9-11.

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