Find the Exact Value by Using a Half-Angle Identity $\cos ( \mathrm { s } + \mathrm { t } )$

Multiple Choice

Find the exact value by using a half-angle identity.
-Find $\cos ( \mathrm { s } + \mathrm { t } )$ given that $\cos \mathrm { s } = \frac { 1 } { 3 }$ , with $\mathrm { s }$ in quadrant $\mathrm { I }$ , and $\sin t = \frac { 1 } { 4 }$ , with $\mathrm { t }$ in quadrant II.

A) $\frac { \sqrt { 15 } - 2 \sqrt { 2 } } { 6 }$
B) $- \frac { \sqrt { 15 } + 2 \sqrt { 2 } } { 6 }$
C) $- \frac { \sqrt { 15 } + 2 \sqrt { 2 } } { 12 }$
D) $\frac { \sqrt { 15 } - 2 \sqrt { 2 } } { 12 }$