Answer
We need to fill in the blank with $\tan$.
Work Step by Step
$$\tan24^\circ=\frac{1}{A66^\circ}\hspace{1cm}(1)$$
From the Cofunction Identity:
$$\tan\theta=\cot(90^\circ-\theta)$$
So $$\tan24^\circ=\cot(90^\circ-24^\circ)=\cot66^\circ$$
Also, from Reciprocal Identity:
$$\cot\theta=\frac{1}{\tan\theta}$$
Therefore, $$\tan24^\circ=\frac{1}{\tan66^\circ}$$
We thus need to fill in the blank with $\tan$.
