If $$\sin m + \sin n = p, \cos m + \cos n = q$$, then find the value of $$\sin m \times \sin n + \cos m \times \cos n$$.

A

$$p^{2} + q^{2} - 2$$

B

$$\frac{(p^{2} + q^{2} - 2)}{2}$$

C

$$p + q - pq$$

D

$$p + q + pq$$