Question

Решите тригонометрическое уравнение
tg²x-tgx-4=0

Answer 1

$tgx = t$
$t^{2} - t - 4 = 0$
$t1 = frac{1 + sqrt{17} }{2}$
$t2 = frac{1 - sqrt{17}}{2}$

$1) tgx = frac{1+sqrt{17}}{2}$
$x = arctan(frac{1+sqrt{17}}{2})$
$2) tgx = frac{1-sqrt{17}}{2}$
$x = arctan(frac{1-sqrt{17}}{2})$