Chapter 7 - Trigonometric Identities and Equations - Summary Exercises Verifying Trigonometric Identities - Exercises - Page 696: 13

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

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