Question

Известно что tga=1, tg(a-b)=3. Найти tgb

Answer 1

Ответ:

tgb=-1/2

Найти tgb.

Answer 2

$tg(\alpha -\beta)=3\\\\\frac{tg\alpha-tg\beta}{1+tg\alpha*tg\beta} =3\\\\\frac{1-tg\beta}{1+tg\beta}-3=0\\\\\frac{1-tg\beta-3-3tg\beta}{1+tg\beta }=0\\\\\frac{-4tg\beta-2 }{1+tg\beta}=0\\\\\left \{ {{-4tg\beta-2=0 } \atop {1+tg\beta\neq0}} \right. \\\\\left \{ {{tg\beta=-0,5 } \atop {tg\beta\neq-1}} \right\\\\Otvet:\boxed{tg\beta=-0,5}$