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.