To solve \( \sin\left(\frac{\pi}{4}\right) + \cos\left(\frac{\pi}{4}\right) \):

1. \( \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \)
2. \( \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \)

Now, adding these two values:

\[
\sin\left(\frac{\pi}{4}\right) + \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} = \frac{2\sqrt{2}}{2} = \sqrt{2}
\]

So, the result is \( \sqrt{2} \).

Would you like a deeper explanation of these steps or any other questions?

### Related Questions:
1. What are the values of \( \sin\left(\frac{\pi}{3}\right) + \cos\left(\frac{\pi}{6}\right) \)?
2. How do you prove the identity \( \sin^2\theta + \cos^2\theta = 1 \)?
3. What is the value of \( \sin\left(\frac{3\pi}{4}\right) + \cos\left(\frac{3\pi}{4}\right) \)?
4. How do you calculate \( \sin\left(\frac{5\pi}{4}\right) + \cos\left(\frac{5\pi}{4}\right) \)?
5. Can you express \( \sin\left(x + \frac{\pi}{4}\right) \) in terms of sine and cosine?

**Tip**: The angles \( \frac{\pi}{4}, \frac{\pi}{6}, \frac{\pi}{3} \) are often encountered in trigonometry, so it's useful to memorize their sine and cosine values.

Learn how to solve the trigonometric problem sin(π/4) + cos(π/4) with a detailed solution. This problem demonstrates the use of special angles in trigonometry, providing a step-by-step explanation. Suitable for students in Grades 9-10.

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