# Solve: tan2x + tan x = 0

## Homework Statement

Solve: tan2x + tan x = 0

I have no idea on how to solve this one =/

Hootenanny
Staff Emeritus
Gold Member

## Homework Statement

Solve: tan2x + tan x = 0

I have no idea on how to solve this one =/
Well what do you think a good first step would be?

berkeman
Mentor
My first inclination would be to take the graph of tan(x), and look visually for a solution (there are likely more than one, but I'd look for the first with x>0.

Then I'd try to use the definition of tan(x) in terms of right triangles to try to get an intuition for how to solve it. If necessary, I'd look into trig substitutions to help solve it, but you might be able to just do it with triangles.

Give it a go....

Hootenanny
Staff Emeritus
Gold Member
if necessary, I'd look into trig substitutions to help solve it, but you might be able to just do it with triangles.
I think that this would be the best way to proceed. There's a very simple trig identity that would let you solve it very quickly ...

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oo would I use the trig identity of: tan(2x) = 2tanx/1-tan^2x ?

how would that factor out though =/ ?

dx
Homework Helper
Gold Member
Factor out tan(x).