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The problem is asking:

**"Which of the following is equal to \( \sin \left(\frac{\pi}{8}\right) \cos \left(\frac{\pi}{8}\right)?"**

We can solve this by using the following trigonometric identity:

\[
\sin(2\theta) = 2 \sin(\theta) \cos(\theta)
\]

By rearranging this equation, we get:

\[
\sin(\theta) \cos(\theta) = \frac{1}{2} \sin(2\theta)
\]

In our case, \(\theta = \frac{\pi}{8}\). Substituting this into the equation:

\[
\sin\left(\frac{\pi}{8}\right) \cos\left(\frac{\pi}{8}\right) = \frac{1}{2} \sin\left(\frac{\pi}{4}\right)
\]

Since \(\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}\), we have:

\[
\sin\left(\frac{\pi}{8}\right) \cos\left(\frac{\pi}{8}\right) = \frac{1}{2} \times \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{4}
\]

Thus, the expression simplifies to \( \frac{\sqrt{2}}{4} \).

Let me know if you'd like further details!

Here are some follow-up questions:

1. What are some other trigonometric identities involving sine and cosine?
2. How would you use the double-angle formula for cosine?
3. Can the identity for sine and cosine be applied to angles other than \(\frac{\pi}{8}\)?
4. What is the value of \(\sin\left(\frac{\pi}{4}\right)\) and why?
5. How can the product of sine and cosine functions be interpreted graphically?

**Tip:** When dealing with trigonometric identities, always look for opportunities to simplify expressions using common identities like the double-angle or Pythagorean identities.

Which of the following is equal to sin(π/8) cos(π/8)?

Learn how to solve sin(π/8) cos(π/8) using trigonometric identities, including the double-angle identity for sine. This solution simplifies the expression to (√2)/4 and explains the steps involved.

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