Write the Product as a Sum or Difference of Trigonometric $\sin ( s + t )$

Multiple Choice

Write the product as a sum or difference of trigonometric functions.
-Find $\sin ( s + t )$ given that $\cos s = - \frac { 1 } { 4 }$ , with $s$ in quadrant III, and $\cos t = - \frac { 3 } { 5 }$ , with $t$ in quadrant III.

A) $\frac { 3 + 4 \sqrt { 15 } } { 20 }$
B) $\frac { 3 - 4 \sqrt { 15 } } { 20 }$
C) $\frac { 3 \sqrt { 15 } + 4 } { 20 }$
D) $\frac { 3 \sqrt { 15 } - 4 } { 20 }$