# Math Help - trigonometry question

1. ## trigonometry question

find all solutions of the equation in the interval [0, 2pi)

tan^2 x + tan x = 0

I am not quite sure how to find the solutions for the tan. I think I am supposed to use the sum and difference formula to solve the problem.

tan(u + v) = (tan u + tan v) / (1 - tan u tan v)

is this correct?

2. Hello, robasc!

Find all solutions in the interval $[0,\:2\pi)\!:\;\;\tan^2\!x + \tan x \:= \:0$
You forgot the most basic method for solving equations:
. . Factor, set each factor equal to zero, and solve.

Factor: . $\tan x(\tan x + 1) \:=\:0$

Then: . $\tan x \:=\:0 \quad\Rightarrow\quad x \:=\:0,\:\pi$

And: . $\tan x + 1 \:=\:0 \quad\Rightarrow\quad \tan x \:=\:-1 \quad\Rightarrow\quad x \:=\;\frac{3\pi}{4},\:\frac{7\pi}{4}$