Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 667: 67

$\dfrac {sec^4\theta -\tan ^{4}\theta }{sec^2\theta +\tan ^{2}\theta }=\sec^2\theta -\tan ^{2}\theta $

$\dfrac {sec^4\theta -\tan ^{4}\theta }{sec^2\theta +\tan ^{2}\theta }=\dfrac {\left( sec^2\theta -\tan ^{2}\theta \right) \left( sec^2\theta +\tan ^{2}\theta \right) }{\left( sec^2\theta +\tan ^{2}\theta \right) }=sec^2\theta -\tan ^{2}\theta $