Question

Вычислите tg165 градусов

Answer 1

$tg165^circ=tg(180^circ-15^circ)=-tg15^circ=-tg(45^circ-30^circ)=\\= -frac{tg45^circ-tg30^circ}{1+tg45^circcdot tg30^circ}=-frac{1-frac{sqrt3}{3}}{1+1cdot frac{sqrt3}{3}} =-frac{(3-sqrt3)cdot 3}{3cdot (3+sqrt3)} =-frac{3-sqrt3}{3+sqrt3} =-frac{(3-sqrt3)^2}{9-3} =\\=-frac{12-6sqrt3}{6}=-frac{6(2-sqrt3)}{6}=-(2-sqrt3)=sqrt3-2$