Simplify to a single trig function with no denominator.

cosecant, theta, dot, cosine, theta

csc*θ*⋅cos*θ*

The expression \( \csc(\theta) \cdot \cos(\theta) \) can be simplified as follows:

Recall that:

\[
\csc(\theta) = \frac{1}{\sin(\theta)}
\]

Substitute this into the expression:

\[
\frac{1}{\sin(\theta)} \cdot \cos(\theta)
\]

This simplifies to:

\[
\frac{\cos(\theta)}{\sin(\theta)}
\]

Now, recall that \( \frac{\cos(\theta)}{\sin(\theta)} \) is equal to \( \cot(\theta) \) (cotangent of \( \theta \)).

So, the simplified expression is:

\[
\boxed{\cot(\theta)}
\]

Let me know if you'd like further details on this or have any other questions!

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Here are 5 related questions to deepen your understanding:
1. How do you derive the identity for \( \cot(\theta) \)?
2. What is the relationship between \( \cot(\theta) \) and other trigonometric functions?
3. How can you express \( \sec(\theta) \cdot \sin(\theta) \) in terms of a single trig function?
4. Can \( \cot(\theta) \) ever be undefined, and under what conditions?
5. How does \( \csc(\theta) \cdot \sin(\theta) \) simplify?

**Tip:** Memorizing the core trigonometric identities like \( \csc(\theta) = \frac{1}{\sin(\theta)} \) and \( \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} \) will help you simplify many complex expressions faster.

Simplify to a single trig function with no denominator: csc(θ) ⋅ cos(θ)

Discover how to simplify the trigonometric expression csc(θ) ⋅ cos(θ) to a single function, cot(θ). This solution involves applying key trigonometric identities such as csc(θ) = 1/sin(θ) and cot(θ) = cos(θ)/sin(θ), making it suitable for high school students in Grades 10-12.

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