1. The problem asks to prove that $\sin(\alpha + \beta) = \sin \gamma$. 2. Normally, the sine addition formula states that $\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$. 3. To prove $\sin(\alpha + \beta) = \sin \gamma$, we need to know the relationship between $\gamma$ and $\alpha, \beta$. Without additional information or constraints relating $\gamma$ to $\alpha$ and $\beta$, this equality cannot be generally proven. 4. If $\gamma = \alpha + \beta$, then by definition $\sin(\alpha + \beta) = \sin \gamma$ holds trivially. 5. Therefore, the statement $\sin(\alpha + \beta) = \sin \gamma$ is true if and only if $\gamma = \alpha + \beta$. 6. Without this condition, the equality does not hold in general. Final answer: $\sin(\alpha + \beta) = \sin \gamma$ if and only if $\gamma = \alpha + \beta$.