Question

Решите 4ctg 30+tg^2 15

Answer 1

$4ctg30^o+tg^215^o=4*sqrt3+frac{1-cos30^o}{1+cos30^o}=4sqrt3+frac{1-frac{sqrt3}{2}}{1+frac{sqrt3}{2}}=4sqrt3+frac{2-sqrt3}{2+sqrt3}=\ =4sqrt3+frac{(2-sqrt3)^2}{4-3}=4sqrt3+4-4sqrt3+3=7$