Question

O conjunto solução da equação tg²x - 1 = 0, com x ϵ [0, 2π[, é:

(a) S= { }
(b) S= {π/4,3π/4,5π/4,7π/4}
(c) S= {π/4,3π/4} (d) S= {5π/4,7π/4}
(e) S= {π/4,5π/4}​​

Answer 1

$\Large\boxed{\begin{array}{l}\sf tg^2(x)-1=0\\\sf tg^2(x)=1\\\sf tg(x)=\pm\sqrt{1}\\\sf tg(x)=\pm1\\\sf tg(x)=1\\\sf x=\dfrac{\pi}{4}~ou~x=\dfrac{5\pi}{4}\\\\\sf tg(x)=-1\\\sf x=\dfrac{3\pi}{4}~ou~x=\dfrac{7\pi}{4}\\\\\sf S=\bigg\{\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{5\pi}{4},\dfrac{7\pi}{4}\bigg\}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\red{\maltese}\blue{~alternativa~b}}}}}\end{array}}$