Calculate: cos(90)cos(45)-sin(90)sin(45)

Expression: $\cos(90^{\circ })\cos(45^{\circ })-\sin(90^{\circ })\sin(45^{\circ })$

Use the following trivial identity

$=0\cdot \frac{\sqrt{2}}{2}-1\cdot \frac{\sqrt{2}}{2}$

Simplify

$=-\frac{\sqrt{2}}{2}$