To solve \(\cos^2(-\pi/4)\), let's follow these steps:

1. **Find \(\cos(-\pi/4)\)**:
   - The cosine function is even, meaning \(\cos(-x) = \cos(x)\). Therefore, \(\cos(-\pi/4) = \cos(\pi/4)\).
   - \(\cos(\pi/4)\) is \(\frac{1}{\sqrt{2}}\).

2. **Square the result**:
   - \(\cos^2(-\pi/4) = \left(\frac{1}{\sqrt{2}}\right)^2 = \frac{1}{2}\).

So, \(\cos^2(-\pi/4) = \frac{1}{2}\).

Would you like more details or have any questions? Here are some related questions to explore:

1. What is the value of \(\sin^2(\pi/4)\)?
2. How does the even property of the cosine function affect its graph?
3. What is the value of \(\cos^2(\pi/3)\)?
4. How do you calculate \(\sin(-\pi/4)\)?
5. What is the Pythagorean identity involving \(\cos^2(x)\) and \(\sin^2(x)\)?

**Tip:** Remember that the square of a trigonometric function always yields a non-negative result.

Explore how to solve cos^2(-pi/4) step-by-step. This problem demonstrates key trigonometric concepts like the even property of cosine and the calculation of cosine squares. Ideal for students in Grades 10-12 learning advanced trigonometry.

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