The cotangent function is defined as the reciprocal of the tangent function,
so we have $\cot 45^\circ = \frac{1}{\tan 45^\circ}$.
Since $\tan 45^\circ = 1$, we have $\cot 45^\circ = \frac{1}{1} = \boxed{1}$.
The answer is: 1
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Find $\cot 45^\circ.$

### Answer:
