Find the Exact Value Under the Given Conditions Find $\cos ( \alpha + \beta )$

Multiple Choice

Find the exact value under the given conditions.
- $\sin \alpha = - \frac { 24 } { 25 } , \pi < \alpha < \frac { 3 \pi } { 2 } ; \quad \tan \beta = - \frac { 2 \sqrt { 21 } } { 21 } , \frac { \pi } { 2 } < \beta < \pi \quad$ Find $\cos ( \alpha + \beta )$ .

A) $\frac { 48 - 7 \sqrt { 21 } } { 125 }$
B) $\frac { 48 + 7 \sqrt { 21 } } { 125 }$
C) $\frac { 14 - 24 \sqrt { 21 } } { 125 }$
D) $\frac { - 14 - 24 \sqrt { 21 } } { 125 }$