To simplify the expression $\sin^2(\theta) \cdot \cot^2(\theta)$ to a single trigonometric function without a denominator, follow these steps:

1. Recall the identity for cotangent: $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$

2. Square cotangent: $\cot^2(\theta) = \frac{\cos^2(\theta)}{\sin^2(\theta)}$

3. Substitute $\cot^2(\theta)$ into the original expression: $\sin^2(\theta) \cdot \cot^2(\theta) = \sin^2(\theta) \cdot \frac{\cos^2(\theta)}{\sin^2(\theta)}$

4. Simplify: The $\sin^2(\theta)$ terms cancel out: $= \cos^2(\theta)$

Thus, the simplified expression is: $\cos^2(\theta)$

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Would you like further details or explanations on any steps?

Here are some related questions for you:

1. How does the identity for cotangent help simplify trigonometric expressions?
2. What happens if the original expression had a secant or tangent term?
3. Can you apply similar steps to simplify other expressions with multiple trigonometric functions?
4. How can Pythagorean identities be used in simplifying trigonometric expressions?
5. What is the relationship between sine and cosine in trigonometric simplifications?

Tip: When simplifying trigonometric expressions, always look for identities that can help you rewrite the functions in simpler forms (like using $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$ or using Pythagorean identities).