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

  • Thread starter Thread starter rought
  • Start date Start date
  • Tags Tags
    Tan
AI Thread Summary
To solve the equation tan(2x) + tan(x) = 0, the first step involves recognizing that tan(2x) can be expressed using the identity tan(2x) = 2tan(x)/(1 - tan^2(x)). Factoring out tan(x) simplifies the equation to tan(x)(2/(1 - tan^2(x)) + 1) = 0. This leads to two cases: either tan(x) = 0 or solving the resulting equation for the second term. Visualizing the graph of tan(x) can also provide insights into potential solutions. Utilizing trigonometric identities and substitutions can facilitate finding the solutions effectively.
rought
Messages
34
Reaction score
0

Homework Statement



Solve: tan2x + tan x = 0


I have no idea on how to solve this one =/
 
Physics news on Phys.org
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).
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Solve the equation: ##\tan x ⋅\tan 4x = 1##
Replies
4
Views
2K
Changing ##\tan\frac{x}{2}## to ##\cos x## for a proof
Replies
8
Views
1K
Solve the given problem involving: ##\tan^{-1} (2x+1)+ \tan^{-1} (2x-1)##
Replies
10
Views
1K
Solving a trigonometric equation with multiples of ##\tan##
Replies
7
Views
2K
Solving an equation for ##x## involving inverse circular functions
Replies
15
Views
2K
Solve the quadratic equation involving sum and product
Replies
2
Views
2K
Is Tan 43° Exactly Equal to (sqrt(5) - 1)/2?
Replies
15
Views
2K
Trigonometric equation solving 2cos x=tan x
Replies
6
Views
3K
Solving sin2x-tan2x=-2(sinx)^2(tan2x) | Proving Identity Step by Step
Replies
8
Views
2K
Solving a Trigonometric Equation
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top