https://file.aiquickdraw.com/mathbot/file/1730289406071l9g5007w.jpg

The expression shown is:

\[
2 \cos^2 \theta - 1
\]

This is a trigonometric identity that can be simplified. Using the double-angle identity for cosine, we know that:

\[
\cos(2\theta) = 2 \cos^2 \theta - 1
\]

Therefore, the expression \(2 \cos^2 \theta - 1\) simplifies to:

\[
\cos(2\theta)
\]

### Final Answer:
\[
2 \cos^2 \theta - 1 = \cos(2\theta)
\]

Would you like further details or have any additional questions?

### Related Questions
1. How do we derive the double-angle identity for cosine?
2. What are some applications of double-angle identities in trigonometry?
3. How can we express \(\sin^2 \theta\) in terms of \(\cos(2\theta)\)?
4. What are the other double-angle identities involving sine and tangent?
5. How can we use \(\cos(2\theta)\) to solve trigonometric equations?

### Tip
Remember that recognizing identities can simplify many trigonometric expressions, making it easier to solve equations or evaluate angles.

Learn how to simplify the trigonometric expression 2cos^2θ - 1 by applying the double-angle identity for cosine. This solution explains the steps to rewrite the expression as cos(2θ), a key concept in trigonometry for Grades 10-12.

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