Answer
Showed that given statement, $( 1- \cos\theta) ( 1+ \cos\theta)$ = $\sin^{2}\theta$,
is an identity as left side transforms into right side.
Work Step by Step
Given statement is-
$( 1- \cos\theta) ( 1+ \cos\theta)$ = $\sin^{2}\theta$
Left Side = $( 1- \cos\theta) ( 1+ \cos\theta)$
= $(1)^{2}$ - $(\cos\theta)^{2}$
[ We know that, $(a)^{2}$ - $(b)^{2}$ = $ ( a- b) ( a+ b) $]
= $1 - \cos^{2}\theta$
= $\sin^{2}\theta$
[ From first Pythagorean identity, $ (1 - \cos^{2}\theta)$ can be written as $\sin^{2}\theta$]
= Right Side
i.e. Left Side transforms into Right Side
i.e. Given statement, $( 1- \cos\theta) ( 1+ \cos\theta)$ = $\sin^{2}\theta$,
is an identity.
