Determine All Solutions of the Equation in Radians $\cos \frac { x } { 2 }$

Determine all solutions of the equation in radians.
-Find $\cos \frac { x } { 2 }$ , given that $\sec x = 4$ and $x$ terminates in $0 < x < \frac { \pi } { 2 }$ .

A) $\frac { \sqrt { 6 } } { 4 }$
B) $\frac { \sqrt { 10 } } { 4 }$
C) $\frac { \sqrt { 8 + 2 \sqrt { 15 } } } { 4 }$
D) $\frac { \sqrt { 8 - 2 \sqrt { 15 } } } { 4 }$