Answer
$\sin^{2}\theta$
Work Step by Step
Given expression is-
$ (1-\cos\theta) (1+\cos\theta)$
= $ 1 + \cos\theta -\cos\theta - \cos^{2}\theta $
( By FOIL method)
= $ 1- \cos^{2}\theta$
= $\sin^{2}\theta$
( Recall first Pythagorean identity)
ALTERNATE METHOD-
Recall that $(A-B) (A+B) = A^{2} - B^{2}$
Therefore $ (1-\cos\theta) (1+\cos\theta)$ = $ 1^{2} - \cos^{2}\theta$
= $\sin^{2}\theta$
