Answer
$1$
Work Step by Step
$\because \csc{\theta} = \dfrac{1}{\sin{\theta}}$
$\therefore \csc{80^{\circ}} = \dfrac{1}{\sin{80^{\circ}}}$
Hence,
$\sin{80^{\circ}} \cdot \csc{80^{\circ}} = \sin{80^{\circ}} \cdot \dfrac{1}{\sin{80^{\circ}}} = \boxed{1}$