Chapter 9 - Analytic Geometry - Section 9.5 Rotation of Axes; General Form of a Conic - 9.5 Assess Your Understanding - Page 698: 1

$\sin (A+B)=\sin (A) \cos(B)+\cos(A) \sin(B)$

We know that the sum formula of two angles, let us say $a$ and $b$, is: $sin (a+b) =\sin(a) \cos(b)+\cos(a) \sin(b)$ Therefore, our result is: $\sin (A+B)=\sin (A) \cos(B)+\cos(A) \sin(B)$