Answer:
[tex]x=\pi n, \ \ \ x=\frac{3\pi}{4}+\pi n[/tex]
Step-by-step explanation:
We express the angle x in radians for all possible values of x:
[tex]x=\pi n\\\\x=\frac{3\pi}{n}+\pi n[/tex]
let tan(x)=u:
[tex]u^2+u=0\\\\u(u+1)=0\\\\u=0,\ u=1[/tex]
#Substitute back u=tan(x)
[tex]tan(x)=0 , \ \ \ or \ tan(x)=-1[/tex]
#We assign for all values of x
[tex]tan(x)=0, \ \ \ \ x=\pi n\\\\tan(x)=-1, \ \ \ \ x=\frac{3\pi}{4}+\pi n[/tex]
#Hence, the equation's solutions are:
[tex]x=\pi n, \ \ \ x=\frac{3\pi}{4}+\pi n[/tex]
