Question

O conjunto verdade da equação sen x + cos x = 0, no intervalo [0; 2pi ]

Answer 1

$\sf sen(x)+cos(x)=0\\\sf sen(x)+cos(x))^2=0^2\\\sf sen^2(x)+2sen(x)cos(x)+cos^2(x)=0\\\sf sen(2x)+1=0\\\sf sen(2x)=-1\\\sf sen(2x)=sen\left(\dfrac{3\pi}{2}\right)\\\sf 2x=\dfrac{3\pi}{2}\\\sf 4x=3\pi\\\sf x=\dfrac{3\pi}{4}$

$\sf s=\{\dfrac{3\pi}{4}\}$