Note that [tex]\displaystyle{ \sin30^{\circ}= \frac{1}{2} [/tex] and [tex]\displaystyle{ \cos30^{\circ}= \frac{ \sqrt{3}}{2} [/tex].
From the unit circle, we can check that [tex]\sin30^{\circ}[/tex] and [tex]\sin(-30)^{\circ}[/tex] have the same value, but opposite signs, that is:
[tex]\sin(-30)^{\circ}=-\sin(30)^{\circ}=-\frac{1}{2}[/tex].
Thus,
[tex]\displaystyle{ \cos(x-y)= \cos(-30^{\circ}-60^{\circ})=cos(-90^{\circ})[/tex].
Note that [tex]cos(-90^{\circ})[/tex] is the x-coordinate of the lowest point on the unit circle, that is (0, -1). Thus [tex]cos(-90^{\circ})=0[/tex]
Answer: 0
