Answer
$${\text{We have proved that }}LHS = RHS$$
Work Step by Step
$$\eqalign{
& \frac{{\cos \theta \tan \theta + \sin \theta }}{{\tan \theta }} = 2\cos \theta \cr
& \cr
& LHS = \frac{{\cos \theta \tan \theta + \sin \theta }}{{\tan \theta }}{\text{ and }}RHS = 2\cos \theta \cr
& \cr
& {\text{Use the identity tan}}\theta = \frac{{\sin \theta }}{{\cos \theta }} \cr
& LHS = \frac{{\cos \theta \left( {\frac{{\sin \theta }}{{\cos \theta }}} \right) + \sin \theta }}{{\frac{{\sin \theta }}{{\cos \theta }}}} \cr
& LHS = \frac{{\sin \theta + \sin \theta }}{{\frac{{\sin \theta }}{{\cos \theta }}}} \cr
& LHS = \frac{{\cos \theta \left( {\sin \theta + \sin \theta } \right)}}{{\sin \theta }} \cr
& LHS = \frac{{2\cos \theta \sin \theta }}{{\sin \theta }} \cr
& LHS = 2\cos \theta \cr
& \cr
& {\text{We have proved that }}LHS = RHS \cr} $$
