Answer
$\cot$ 30$^{\circ}$ $\lt$ $\tan$ 40$^{\circ}$ is false.
Work Step by Step
$\cot$ 30 < $\tan$ 40
We must first get the inequality in terms of $\cot$
$\tan$ $A$ = $\cot$ (90$^{\circ}$ - $A$)
Therefore:
$\tan$ 40 = $\cot$(90$^{\circ}$ - 41$^{\circ}$)
$\tan$ 40 = $\cot$ 50$^{\circ}$
The inequality could be rewritten: $\cot$ 30$^{\circ}$
< $\cot$ 50$^{\circ}$
From 0$^{\circ}$ to 90$^{\circ}$, as the angle increases, the $cotangent$ of the angle decreases.
Therefore: $\cot$ 30$^{\circ}$ $\lt$ $\cot$ 50$^{\circ}$ is false.
Therefore: $\cot$ 30$^{\circ}$ $\lt$ $\tan$ 40$^{\circ}$ is false.
