Using Addition property:
[tex]cos(135 + 120) = cos(135) \cdot cos(120) - sin(135) \cdot sin(120)[/tex]
[tex]cos(135) = cos(45 + 90) = -cos(45) = -\frac{1}{\sqrt{2}}[/tex]
[tex]cos(120) = cos(180 - 60) = -cos(60) = -\frac{1}{2}[/tex]
[tex]sin(135) = sin(45 + 90) = sin(45) = \frac{1}{\sqrt{2}}[/tex]
[tex]sin(120) = sin(180 - 60) = sin(60) = \frac{\sqrt{3}}{2}[/tex]
[tex]\therefore cos(135 + 120) = [-\frac{1}{\sqrt{2}} \cdot -\frac{1}{2}] - [\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2}][/tex]
[tex]= \frac{1}{2\sqrt{2}} - \frac{\sqrt{3}}{2\sqrt{2}}[/tex]
[tex]= \frac{1 - \sqrt{3}}{2\sqrt{2}}[/tex]
