Master the Equation: Solving tan2x + tan x = 0 | Expert Tips & Tricks

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Homework Help Overview

The discussion revolves around solving the equation tan(2x) + tan(x) = 0, which falls under the subject area of trigonometry. Participants are exploring various approaches to tackle this equation without providing a complete solution.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss visualizing the problem using the graph of tan(x) to identify potential solutions. There are considerations of using the definition of tan(x) in terms of right triangles and the possibility of employing trigonometric substitutions. Questions arise about the application of specific trigonometric identities and how to factor the equation.

Discussion Status

The discussion is active, with participants offering different strategies and questioning the best first steps to take. Some guidance has been provided regarding factoring and the use of trigonometric identities, but no consensus has been reached on a definitive approach.

Contextual Notes

Participants express uncertainty about the initial steps and the application of trigonometric identities, indicating a need for clarification on these concepts. There is also a mention of potential multiple solutions to the equation.

rought
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Homework Statement



Solve: tan2x + tan x = 0


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

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?
 
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...
 
berkeman said:
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 ... :wink:
 
Last edited by a moderator:
oo would I use the trig identity of: tan(2x) = 2tanx/1-tan^2x ?

how would that factor out though =/ ?
 
Factor out tan(x).
 

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