Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 960: 27

Option $B$

$\cot \theta +\tan \theta =\dfrac{\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{\sin \theta}$ $=\dfrac{\sin^2 \theta+\cos^2 \theta}{\sin \theta \cos \theta}$ $=\dfrac{1}{\sin \theta \cos \theta}$ $=\dfrac{2}{ 2 \sin \theta \cos \theta}$ $=2 \csc 2\theta$ Hence, we can see that only option $B$ satisfies the equation.