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