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