Official solution
\[\cos255^\circ = \cos(270^\circ-15^\circ) = -\sin15^\circ, \qquad \sin195^\circ = \sin(180^\circ+15^\circ) = -\sin15^\circ\]
\[\cos255^\circ+\sin195^\circ = -2\sin15^\circ = -2\cdot\frac{\sqrt{3}-1}{2\sqrt{2}} = -\frac{\sqrt{3}-1}{\sqrt{2}}\]