Answer
Showed that given statement, $ \cos\theta( \sec\theta - \cos\theta) $ = $\sin^{2}\theta$,
is an identity as left side transforms into right side.
Work Step by Step
Given statement is-
$ \cos\theta( \sec\theta - \cos\theta) $ = $\sin^{2}\theta$
Left Side = $ \cos\theta( \sec\theta - \cos\theta) $
= $ \cos\theta $ $( \frac{1}{\cos\theta} - \cos\theta) $
(Using reciprocal identity for $\sec\theta$)
= $ 1 - \cos^{2}\theta $
= $\sin^{2}\theta$
( Using first Pythagorean identity)
= Right Side
i.e. Left Side transforms into Right Side
i.e. Given statement, $ \cos\theta( \sec\theta - \cos\theta) $ = $\sin^{2}\theta$,
is an identity.
