Question

Como resolver

Tg²x-1=0

Answer 1

$\Large\boxed{\begin{array}{l}\sf tg^2x-1=0\\\sf tg^2x=1\\\sf tg\,x=\pm\sqrt{1}\\\sf tg\,x=\pm1\\\sf tg\,x=1\\\sf\iff x=\dfrac{\pi}{4}+k\pi~ou~x=\dfrac{5\pi}{4}+k\pi,k\in\mathbb{Z}\\\\\sf tg(x)=-1\\\sf\iff x=\dfrac{3\pi}{4}+k\pi~ou~x=\dfrac{7\pi}{4}+k\pi,k\in\mathbb{Z}\end{array}}$