To simplify the expression \( \sin(x) + \sin(-x) \), we can use the property of the sine function:

\[
\sin(-x) = -\sin(x)
\]

Substituting this into the expression gives:

\[
\sin(x) + \sin(-x) = \sin(x) - \sin(x) = 0
\]

Therefore, the final result is:

\[
\sin(x) + \sin(-x) = 0
\]

If you have any questions or need further details, feel free to ask! Here are some related questions you might find interesting:

1. What other trigonometric identities involve negative angles?
2. How does the sine function behave over different intervals?
3. Can you derive the sine addition formula from basic identities?
4. What is the graphical representation of \( \sin(x) \) and \( \sin(-x) \)?
5. How do sine and cosine functions relate to the unit circle?

**Tip:** Remember that sine is an odd function, which means that \( \sin(-x) = -\sin(x) \) holds true for all \( x \).

Learn how to simplify the expression sin(x) + sin(-x) using the odd function property of sine. This problem covers core trigonometric concepts and helps students understand function behaviors with negative angles. Suitable for Grades 10-12.

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