Find the value of $$\frac{\cos 30^\circ - \sin 30^\circ}{\sin 60^\circ + \cos 60^\circ}$$

$$\frac{\cos 30^\circ - \sin 30^\circ}{\sin 60^\circ + \cos 60^\circ}$$ = $$\frac{\frac{\sqrt{3}}{2}-\frac{1}{2}}{\frac{\sqrt{3}}{2}+\frac{1}{2}}$$

= $$\frac{\frac{\sqrt{3}-1}{2}}{\frac{\sqrt{3}+1}{2}}$$

= $$\frac{\sqrt{3}-1}{\sqrt{3}+1}$$

= $$\frac{\sqrt{3}-1}{\sqrt{3}+1}\times\frac{\sqrt{3}-1}{\sqrt{3}-1}$$

= $$\frac{\left(\sqrt{3}\right)^2+1^2-2.\sqrt{3}.1}{\left(\sqrt{3}\right)^2-1^2}$$

= $$\frac{3+1-2\sqrt{3}}{3-1}$$

= $$\frac{4-2\sqrt{3}}{2}$$

= $$2-\sqrt{3}$$

Hence, the correct answer is Option A