Chapter 9 - Analytic Geometry - Section 9.5 Rotation of Axes; General Form of a Conic - 9.5 Assess Your Understanding - Page 698: 2

$\sin (2 \theta)=2 \sin (\theta) \cos(\theta)$

We know that the double angle formula for $\sin$ is: $\sin (2x) =2 \sin x\cos x$ Here, $x=\theta$ Therefore, our result is: $\sin (2 \theta)=2 \sin (\theta) \cos(\theta)$