sin α cos β = 1/2, range of cos α sin β ? (trigonometry)

$\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) = \\ \dfrac 1 2 + \cos(\alpha)\sin(\beta)\\ \cos(\alpha)\sin(\beta) = \sin(\alpha+\beta)-\dfrac 1 2$

$\text{You should know the range of }\sin(\alpha +\beta)\\ \text{So what is the range of }\sin(\alpha +\beta)-\dfrac 1 2$