Question

Розв'яжіть рівняння.
$tg ^{2} x - 2tgx - 3 = 0$
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Answer 1

$\tg {}^{2} (x) - 2 \tg(x) - 3 = 0 \\ \tg(x) = t \\ {t}^{2} - 2t - 3 = 0 \\ \left[ \begin{gathered} t_{1} = 3 \\ t_{2} = - 1 \end{gathered} \right. \\ \left[ \begin{gathered} \tg(x) = 3 \\ \tg(x) = - 1 \end{gathered} \right. \\ \left[ \begin{gathered} x = \arctg(3) + \pi n \\ x = - \frac{\pi}{4} + \pi k, \: n,k \in \mathbb Z \end{gathered} \right.$