Correct Answer: $\frac{\sqrt{3}}{2}$

Solution :
Given: In $\triangle {XYZ}$, right-angled at $Y$.
We know that the sum of all the angles in a triangle is 180°.
$\sin X = \frac{1}{2}$
⇒ $\sin X = \sin{30°}$
So, $\angle X = 30°$
Then $\angle Z = 60°$, because $\angle Y + \angle X + \angle Z = 180°$
Then, $\cos X \cos Z + \sin X \sin Z$
$=\cos 30° \cos 60° + \sin 30° \sin 60°$
$=\frac{\sqrt{3}}{2} × \frac{1}{2} + \frac{1}{2} × \frac{\sqrt{3}}{2}$
$ = \frac{\sqrt{3}}{2}$
Hence, the correct answer is $\frac{\sqrt{3}}{2}$.