Question

Tan x tan x + tan x = 0

Answer 1

Answer:

$x=\pi n, \ \ \ x=\frac{3\pi}{4}+\pi n$

Step-by-step explanation:

We express the angle x in radians for all possible values of x:

$x=\pi n\\\\x=\frac{3\pi}{n}+\pi n$

let tan(x)=u:

$u^2+u=0\\\\u(u+1)=0\\\\u=0,\ u=1$

#Substitute back u=tan(x)

$tan(x)=0 , \ \ \ or \ tan(x)=-1$

#We assign for all values of x

$tan(x)=0, \ \ \ \ x=\pi n\\\\tan(x)=-1, \ \ \ \ x=\frac{3\pi}{4}+\pi n$

#Hence, the equation's solutions are:

$x=\pi n, \ \ \ x=\frac{3\pi}{4}+\pi n$