#### Answer

$\sec75^\circ36'$ is the co-function in need to find in this exercise.

#### Work Step by Step

$$\csc(14^\circ24')$$
First, we must claim that secant is the co-function of cosecant.
Then we find the complementary angle $\theta$ for secant to rewrite $\csc(14^\circ24')$, which must satisfy
$$\sec\theta=\csc(14^\circ24')\hspace{1cm}(1)$$
According to Co-function Identity: $\sec\theta=\csc(90^\circ-\theta)$
Apply this to the equation $(1)$:
$$\csc(90^\circ-\theta)=\csc(14^\circ24')$$
$$90^\circ-\theta=14^\circ24'$$
$$\theta=90^\circ-14^\circ24'=75^\circ36'$$
$\sec75^\circ36'$ is thus the co-function in need to find here.