Question

Verificați egalitatea tg105°=tg(60°+45°)= -2-√3

Answer 1

[tex]Aplicam\ formula:tg(a+b)=\frac{tga+tgb}{1-tga\cdot tgb}\\ tg105=tg(45+60)=\frac{tg45+tg60}{1-tg45\cdot tg60}\\ Deci:tg105=\frac{1+\sqrt{3}}{1-\sqrt{3}}\\ Rationalizam:tg105=\frac{(1+\sqrt{3})^2}{(1-\sqrt3)(1+\sqrt3)}=\frac{1+2\sqrt{3}+3}{1-3}=\frac{4+2\sqrt{3}}{-2}=-2-\sqrt{3}[/tex]