u and v are unit vectors, so |u| = |v| = 1.
We are also told that u + v is a unit vector, so
$\displaystyle (u + v) \cdot (u + v) = |u + v|^2 = 1$
(Since for any vector x, $\displaystyle x \cdot x = x^2$.)
But
$\displaystyle (u + v) \cdot (u + v) = u^2 + v^2 + 2 u \cdot v$
What can you make of all this?
-Dan