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rought
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Homework Statement
Solve: tan2x + tan x = 0
I have no idea on how to solve this one =/
Master the Equation: Solving tan2x + tan x = 0 | Expert Tips & Tricks
- Thread starter rought
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SUMMARY
The equation tan2x + tan x = 0 can be solved by factoring out tan x, leading to the simplified form tan x (tan x + 1) = 0. This results in two solutions: tan x = 0 and tan x = -1. Utilizing the trigonometric identity tan(2x) = 2tan x / (1 - tan^2 x) can further assist in understanding the behavior of the function. Visualizing the graph of tan(x) can also provide insights into the solutions.
PREREQUISITES- Understanding of trigonometric identities, specifically tan(2x) = 2tan x / (1 - tan^2 x)
- Basic knowledge of factoring algebraic expressions
- Familiarity with the properties of the tangent function
- Graphing skills for visualizing trigonometric functions
- Study the derivation and applications of the trigonometric identity tan(2x) = 2tan x / (1 - tan^2 x)
- Practice factoring trigonometric equations
- Explore the graphical representation of the tangent function and its periodicity
- Learn about trigonometric substitutions in solving equations
Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their problem-solving skills in trigonometric equations.
Solve: tan2x + tan x = 0
I have no idea on how to solve this one =/
- #2
Hootenanny
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Well what do you think a good first step would be?rought said:
- #3
berkeman
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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...
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...
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Hootenanny
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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 ...berkeman said:
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- #5
rought
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oo would I use the trig identity of: tan(2x) = 2tanx/1-tan^2x ?
how would that factor out though =/ ?
how would that factor out though =/ ?
- #6
dx
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Factor out tan(x).
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