Decide Whether the Expression Is or Is Not an Identity $\cos \frac { \theta } { 2 }$

Multiple Choice

Decide whether the expression is or is not an identity.
-Find $\cos \frac { \theta } { 2 }$ , given that $\sin \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in $0 < \theta < 90 ^ { \circ }$ .

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