Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.5 Write Trigonometric Functions and Models - 14.5 Exercises - Quiz for Lessons 14.3-14.5 - Page 945: 2

$\csc \theta$

Here, we have $\sin \theta(1+\cot^2 \theta)$ Re-arrange the given equation as: $=\sin \theta (\csc^2 \theta)$ $=\sin \theta \times \csc \theta \times \csc \theta$ $=\dfrac{\sin \theta}{\sin \theta} \times \csc \theta$ $=\csc \theta$