Question

Помогите:)Вычислить ctg15 +1 / 2ctg15

Answer 1

$ctg15=ctg(45-30)=frac{cyg45cdot ctg30+1}{ctg45-ctg30}=frac{1cdot sqrt3+1}{1-sqrt3}=frac{1+sqrt3}{1-sqrt3}\\\frac{ctg15+1}{2ctg15}=frac{frac{1+sqrt3}{1-sqrt3}+1}{2cdot frac{1+sqrt3}{1-sqrt3}}=frac{1+sqrt3+1-sqrt3}{(1-sqrt3)cdot frac{2(1+sqrt3)}{1-sqrt3}}=frac{2}{2(1+sqrt3)}=frac{1}{1+sqrt3}=\\=frac{1-sqrt3}{(1+sqrt3)(1-sqrt3)}= frac{1-sqrt3}{1-3}=frac{1-sqrt3}{-2}=frac{sqrt3-1}{2}$