#### Answer

$\cot(-84^\circ03')$ is the answer in this exercise.

#### Work Step by Step

$$\tan174^\circ03'$$
Cotangent and tangent are cofunctions. So to write $\tan174^\circ03'$ in terms of cofunction, cotangent would be included.
Now the job is to figure out the value of $\theta$, which must satisfy
$$\cot\theta=\tan174^\circ03'\hspace{1cm}(1)$$
According to Cofunction Identity: $\cot\theta=\tan(90^\circ-\theta)$
Apply this to the equation $(1)$:
$$\tan(90^\circ-\theta)=\tan174^\circ03'$$
$$90^\circ-\theta=174^\circ03'$$
$$\theta=90^\circ-174^\circ03'=-84^\circ03'$$
$\cot(-84^\circ03')$ is overall the answer to this exercise.