[latex]cos135^o=cos(90^o+45^o)=-sin45^o=-\frac{\sqrt2}{2}\\\\reduction\ formulas:\ cos(90^o+\alpha)=-sin\alpha[/latex]

[latex]cos(180^0- \alpha )=-cos \alpha \\ \\ cos135^0=cos(180^0-45^0)=-cos45^0=- \frac{ \sqrt{2} }{2} [/latex]