Can somebody explain to me why the line $DB$ is equal to $\sin(\alpha + \beta)$. I haven't been able to figure it out. My image (which I would post if I could) is located here:
For example,
if I try to use the law of cosines then, $(\cos \alpha)^2 + (\cos \beta)^2 - 2(\cos \alpha) (\cos \beta) (\cos(\alpha + \beta)) = DB$ which does not obviously equal $\sin(\alpha + \beta)$.