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

Multiple Choice

Find the exact value under the given conditions.
- $\cos \alpha = - \frac { 4 } { 5 } , \frac { \pi } { 2 } < \alpha < \pi ; \quad \sin \beta = - \frac { \sqrt { 21 } } { 5 } , \pi < \beta < \frac { 3 \pi } { 2 } \quad$ Find $\cos ( \alpha + \beta )$ .

A) $\frac { - 6 + 4 \sqrt { 21 } } { 25 }$
B) $\frac { 8 + 3 \sqrt { 21 } } { 25 }$
C) $\frac { 6 - 4 \sqrt { 21 } } { 25 }$
D) $\frac { - 8 - 3 \sqrt { 21 } } { 25 }$