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Let's solve the given trigonometric expression:

Given expression:
\[
\sin \theta (\csc \theta - \sin \theta)
\]

We know that:
\[
\csc \theta = \frac{1}{\sin \theta}
\]

Substitute this into the expression:
\[
\sin \theta \left(\frac{1}{\sin \theta} - \sin \theta\right)
\]

Now, distribute \(\sin \theta\) inside the parentheses:
\[
\sin \theta \times \frac{1}{\sin \theta} - \sin \theta \times \sin \theta
\]

This simplifies to:
\[
1 - \sin^2 \theta
\]

We know that:
\[
1 - \sin^2 \theta = \cos^2 \theta \quad \text{(using the Pythagorean identity: \(\sin^2 \theta + \cos^2 \theta = 1\))}
\]

So the final simplified expression is:
\[
\cos^2 \theta
\]

Thus, the correct answer is **(a) \(\cos^2 \theta\)**.

Would you like further details or have any questions about this problem?

Here are 5 related questions to deepen your understanding:

1. How can you derive the Pythagorean identity from the unit circle?
2. What are the other forms of trigonometric identities involving \(\cos^2 \theta\)?
3. How do you express \(\cot \theta\) in terms of sine and cosine?
4. How would the identity change if you were to work with \(\sec \theta\) instead?
5. What is the significance of \(\csc \theta\) in trigonometric equations?

**Tip:** Always double-check the identities you apply by referencing known formulas, such as the Pythagorean identity, to avoid errors.

Learn how to simplify the trigonometric expression sinθ(cscθ - sinθ) using key trigonometric identities. This problem is suitable for students in Grades 9-11 and involves concepts like cscθ and the Pythagorean identity.

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