Answer
$1$
Work Step by Step
We know that $\sec(\theta)=\csc(90^{\circ}-\theta)$.
Hence,
$\frac{\sec(55^{\circ})}{\csc(35^{\circ})}\\
=\frac{\sec(55^{\circ})}{\csc(90^{\circ}-35^{\circ})}\\
=\frac{\sec(55^{\circ})}{\sec(55^{\circ})}\\
=1$