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