Chapter 7 - Trigonometric Identities and Equations - 7.1 Fundamental Identities - 7.1 Exercises - Page 659: 63

$-\cot \theta +1$

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