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