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.