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The given expression is:

\[
\cot\left(\frac{\pi}{2} - \theta\right) \cdot \csc(\theta)
\]

Using the co-function identity for cotangent:

\[
\cot\left(\frac{\pi}{2} - \theta\right) = \tan(\theta)
\]

This simplifies the expression to:

\[
\tan(\theta) \cdot \csc(\theta)
\]

Now, we know that \(\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\) and \(\csc(\theta) = \frac{1}{\sin(\theta)}\). Substituting these into the expression gives:

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

Thus, the expression simplifies to:

\[
\sec(\theta)
\]

So the final answer is:

\[
\sec(\theta)
\]

Do you want more details or have any questions? Here are 5 related questions:

1. What is the co-function identity for \(\sin\left(\frac{\pi}{2} - \theta\right)\)?
2. How does the identity for \(\tan(\theta)\) relate to \(\cot(\theta)\)?
3. What is the difference between secant and cosine in terms of their definitions?
4. How would the expression change if it were \(\cot(\theta) \cdot \csc\left(\frac{\pi}{2} - \theta\right)\)?
5. Can you derive the identity for \(\sec(\theta)\) using right triangles?

**Tip:** Understanding co-function identities (like \(\sin\left(\frac{\pi}{2} - \theta\right) = \cos(\theta)\)) helps in simplifying many trigonometric expressions!

Rewrite the expression cot(π/2 - θ) csc(θ) as one of the six trigonometric functions of acute angle θ.

Learn how to simplify the expression cot(π/2 - θ) csc(θ) into one of the six trigonometric functions by using co-function identities and simplifying trigonometric expressions. Suitable for high school students in Grades 9-12.

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