Chapter 7 - Trigonometric Identities and Equations - Summary Exercises Verifying Trigonometric Identities - Exercises - Page 696: 1

$\tan \theta +\cot \theta =\dfrac {1}{\cos \theta \sin \theta }=sec\theta csc\theta $

$\tan \theta +\cot \theta =\dfrac {\sin \theta }{\cos \theta }+\dfrac {\cos \theta }{\sin \theta }=\dfrac {\cos ^{2}\theta +\sin ^{2}\theta }{\cos \theta \sin \theta }=\dfrac {1}{\cos \theta \sin \theta }=sec\theta csc\theta $