Question

Calcule tg b, sabendo que tg(a-b) = √3 e tg a=1

Answer 1

$tg(a-b)=\frac{tg a - tg b}{1+tga \cdot tg b} \\ \frac{tg a - tg b}{1+tga \cdot tg b}=\sqrt3 \\ \frac{1 - tg b}{1+tg b}=\sqrt3 \\ \sqrt3 \cdot (1+tgb)=1-tgb \\ \sqrt3+\sqrt3\cdot tgb =1-tgb \\ (\sqrt3-1)tgb=1-\sqrt3 \\ tgb= \frac{1-\sqrt3}{\sqrt3-1}$