Помогите:)Вычислить ctg15 +1 / 2ctg15

[latex]ctg15=ctg(45-30)=\frac{cyg45\cdot ctg30+1}{ctg45-ctg30}=\frac{1\cdot \sqrt3+1}{1-\sqrt3}=\frac{1+\sqrt3}{1-\sqrt3}\\\\\\\frac{ctg15+1}{2ctg15}=\frac{\frac{1+\sqrt3}{1-\sqrt3}+1}{2\cdot \frac{1+\sqrt3}{1-\sqrt3}}=\frac{1+\sqrt3+1-\sqrt3}{(1-\sqrt3)\cdot \frac{2(1+\sqrt3)}{1-\sqrt3}}=\frac{2}{2(1+\sqrt3)}=\frac{1}{1+\sqrt3}=\\\\=\frac{1-\sqrt3}{(1+\sqrt3)(1-\sqrt3)}= \frac{1-\sqrt3}{1-3}=\frac{1-\sqrt3}{-2}=\frac{\sqrt3-1}{2} [/latex]