Question

ТРИГОНОМЕТРИЯ. СРОЧНО!
Найти tg$alpha$, если tg2$alpha$= $frac{1}{3}$

Answer 1

$tg2 alpha = frac{2tg alpha }{1 - tg^{2} alpha}$
$frac{1}{3} = frac{2tg alpha }{1 - tg^{2} alpha}$
$1 - tg^{2} alpha = 6tg alpha$
$tg^{2} alpha + 6tg alpha - 1 = 0$
Пусть t = tgα.
$t ^{2} + 6t - 1 = 0$
t₁ + t₂ = -6
t₁*t₂ = -1

t₁ = -3
t₂ = 2

Значит, tgα = -3, tgα = 2.