Let's break down the expression step by step:

The expression is:
\[
\cos 60^\circ + \sin 30^\circ - \cos 30^\circ
\]

Using known trigonometric values:

- \(\cos 60^\circ = \frac{1}{2}\)
- \(\sin 30^\circ = \frac{1}{2}\)
- \(\cos 30^\circ = \frac{\sqrt{3}}{2}\)

Now substitute these values into the expression:
\[
\frac{1}{2} + \frac{1}{2} - \frac{\sqrt{3}}{2}
\]

Simplifying:
\[
1 - \frac{\sqrt{3}}{2}
\]

So, the final answer is:
\[
1 - \frac{\sqrt{3}}{2}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the value of \(\sin 60^\circ\)?
2. How is the unit circle related to trigonometric functions?
3. Can you express \(\cos 30^\circ\) in decimal form?
4. What is the Pythagorean identity for sine and cosine?
5. How would you calculate the tangent of 30°?

**Tip**: Memorizing common trigonometric values for angles like 30°, 45°, and 60° can significantly speed up solving problems.

Learn how to simplify the trigonometric expression cos 60° + sin 30° - cos 30° by applying known values for special angles. This solution explains key trigonometric concepts and is suitable for students in Grades 9-12.

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