Answer
$\cos^{2}\theta - 4 \cos\theta + 4$
Work Step by Step
Given expression-
$(\cos\theta - 2)^{2}$
= $(\cos\theta - 2) (\cos\theta - 2)$
(Recall $a^{2} = a\times a$)
= $\cos\theta. \cos\theta - 2 \cos\theta - 2\cos\theta + 4 $
(By FOIL method)
= $\cos^{2}\theta - 4 \cos\theta + 4 $
ALTERNATE METHOD
Recall $ (A-B)^{2} = A^{2} - 2 AB + B^{2}$
Therefore-
$(\cos\theta - 4)^{2} = \cos^{2}\theta - 2 \cos\theta .2 + 2^{2}$
= $\cos^{2}\theta - 4 \cos\theta + 4$
