Answer
$1$
Work Step by Step
Recall the co-function identity:
$ \tan (\theta)=\cot(90^{\circ}-\theta)$
Therefore, $\dfrac{\cos (10^{\circ})}{\sin (80^{\circ})}
\\=\dfrac{\cos \ 10^{\circ}}{\cos(90^{\circ}-80^{\circ})}
\\=\dfrac{\cos \ 10^{\circ}}{\cos \ 10^{\circ}}
\\=1$