## Trigonometry 7th Edition

Showed that given statement, $\tan^{2}\theta + 1$ = $\sec^{2}\theta$, is an identity as left side transforms into right side.
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.