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The expression you provided, \( 2\cos^2 \theta - 1 \), is a well-known trigonometric identity. It can be simplified using the double-angle identity for cosine.

### Simplification Using Trigonometric Identities:
\[
2\cos^2 \theta - 1 = \cos(2\theta)
\]

This is known as the double-angle formula for cosine:
\[
\cos(2\theta) = 2\cos^2 \theta - 1
\]

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

Would you like more details on how this identity works or applications of this formula? 

### Related Questions
1. How is the double-angle formula for cosine derived?
2. What other trigonometric identities are related to \(\cos(2\theta)\)?
3. How can we use this identity in solving trigonometric equations?
4. Can we express \(2\cos^2 \theta - 1\) in terms of sine?
5. What are other forms of the double-angle identities?

### Tip
Memorizing fundamental trigonometric identities like the double-angle formulas can significantly simplify solving trigonometric problems.

Discover how to simplify the expression 2cos^2θ - 1 using trigonometric identities. This solution explores the double-angle formula for cosine, helping students understand key trigonometric transformations. Ideal for Grades 10-12.

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