Answer
The required value is $\frac{1}{2}$
Work Step by Step
We use the identity for $\sin \left( C-D \right)$:
$sin\left( C-D \right)=\sin C\text{cos }D-\cos C\sin D$.
Thus, we apply the difference formula in the given expression:
$\begin{align}
& \sin {{80}^{\circ }}\cos {{50}^{\circ }}-\cos {{80}^{\circ }}\sin {{50}^{\circ }}=\sin \left( {{80}^{\circ }}-{{50}^{\circ }} \right) \\
& =\sin {{30}^{\circ }} \\
& =\frac{1}{2}
\end{align}$
