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To solve for \( \cos 45^\circ \), we use the fact that:

\[
\cos 45^\circ = \frac{\sqrt{2}}{2}
\]

Thus, the correct answer from the list provided in your image is:

\[
\boxed{\frac{\sqrt{2}}{2}}
\]

Would you like further details or explanations on this? Here are some related questions to explore:

1. What are the values of \( \sin 45^\circ \) and \( \tan 45^\circ \)?
2. How do we derive the trigonometric values for special angles like 30°, 45°, and 60°?
3. What is the unit circle, and how does it help in understanding trigonometric functions?
4. How does the value of \( \cos 45^\circ \) relate to a 45°-45°-90° triangle?
5. Can you explain how to compute cosine values for angles that are not part of the standard trigonometric table?

**Tip:** Memorizing the key trigonometric ratios for 30°, 45°, and 60° can help quickly solve many problems without needing a calculator.

Learn how to determine the value of \( \cos 45^\circ \). This problem focuses on trigonometry and special angles, specifically the cosine of 45 degrees, which is \( \frac{\sqrt{2}}{2} \). Suitable for high school students, Grades 9-12.

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