[tex]\it tg15^o=tg(45^o-30^o)=\dfrac{tg45^o-tg30^o}{1+tg45^otg30^o}=\dfrac{1-\dfrac{\sqrt3}{3}}{1+1\cdot\dfrac{\sqrt3}{3}}=\dfrac{^{3-\sqrt3)}3-\sqrt3}{\ \ 3+\sqrt3}=\\ \\ \\ =\dfrac{(3-\sqrt3)^2}{(3-\sqrt3)(3+\sqrt3)}=\dfrac{9-6\sqrt3+3}{9-3}=\dfrac{12-6\sqrt3}{6}=\dfrac{6(2-\sqrt3)}{6}=2-\sqrt3[/tex]
