## Trigonometry 7th Edition

Showed that given statement, $(\cos\theta + 1) ( \cos\theta- 1)$ = - $\sin^{2}\theta$, is an identity as left side transforms into right side.
Given statement is- $(\cos\theta + 1) ( \cos\theta- 1)$ = - $\sin^{2}\theta$ Left Side = $(\cos\theta + 1) ( \cos\theta- 1)$ = $(\cos\theta)^{2}$ - $(1)^{2}$ [ We know that, $(a)^{2}$ - $(b)^{2}$ = $( a + b) ( a - b)$] = $\cos^{2}\theta - 1$ = - ($1 - \cos^{2}\theta$) = - $\sin^{2}\theta$ [ 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, $( \cos\theta + 1) ( \cos\theta- 1)$ = - $\sin^{2}\theta$, is an identity.