Chapter 7 - Trigonometric Identities and Equations - 7.1 Fundamental Identities - 7.1 Exercises - Page 659: 78

$-\tan ^{2}\theta $

$-sec^{2}\left( -\theta \right) +\sin ^{2}\left( -\theta \right) +\cos ^{2}\left( -\theta \right) =-sec^{2}\left( -\theta \right) +1=1-\dfrac {1}{\cos ^{2}\left( -\theta \right) }=1-\dfrac {1}{\cos ^{2}\theta }=\dfrac {\cos ^{2}\theta -1}{\cos ^{2}\theta }=\dfrac {-\sin ^{2}\theta }{\cos ^{2}\theta }=-\tan ^{2}\theta $