The expression you provided is \(\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)\).

This expression represents the inverse cosine (or arccosine) of \(\frac{\sqrt{2}}{2}\).

### Solution:
To find the value of \(\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)\), we need to determine the angle whose cosine is \(\frac{\sqrt{2}}{2}\).

We know that:
\[
\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}
\]

Therefore:
\[
\cos^{-1}\left(\frac{\sqrt{2}}{2}\right) = \frac{\pi}{4} \text{ radians}
\]
Or equivalently:
\[
\cos^{-1}\left(\frac{\sqrt{2}}{2}\right) = 45^\circ
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the value of \(\cos^{-1}(0)\)?
2. How do you solve \(\cos^{-1}\left(\frac{1}{2}\right)\)?
3. What is the domain of the inverse cosine function?
4. How can you express \(\cos^{-1}\) in terms of trigonometric identities?
5. What is the difference between \(\cos^{-1}\) and \(\sec^{-1}\)?

### Tip:
The inverse trigonometric functions return the angle that corresponds to a given trigonometric ratio, typically within a specific range.

Understand how to calculate the inverse cosine of √2/2, a common problem in trigonometry. This solution provides a step-by-step approach to finding the angle that corresponds to cos^{-1}(√2/2), using key trigonometric concepts. Ideal for students in Grades 9-12.

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