Chapter 7 - Trigonometric Identities and Equations - 7.1 Fundamental Identities - 7.1 Exercises - Page 659: 76

$-\sin \theta $

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