Question

Resolva a equação , talque 0 ≤ x < 2π:
tg^2 x = 3

Answer 1

$\sf{tg^2(x)=3}\\\sf{tg(x)=\pm\sqrt{3}}\\\sf{tg(x)=\sqrt{3}\implies~x=\dfrac{\pi}{3}~~ou~~x=\dfrac{4\pi}{3}}\\\sf{tg(x)=-\sqrt{3}\implies~x=\dfrac{2\pi}{3}~~ou~~x=\dfrac{5\pi}{3}}$

$\sf{S=\Bigg\{\dfrac{\pi}{3},\dfrac{4\pi}{3},\dfrac{2\pi}{3},\dfrac{5\pi}{3}\Bigg\}}$