Answer
$cos~72^{\circ} = \frac{\sqrt{5}-1}{4}$
Work Step by Step
$cos~x = sin(90^{\circ}-x)$
We can find the value of $cos~72^{\circ}$:
$cos~72^{\circ} = sin(90^{\circ}-72^{\circ})$
$cos~72^{\circ} = sin(18^{\circ})$
$cos~72^{\circ} = \frac{\sqrt{5}-1}{4}$