anonymous
  • anonymous
Find the general solution of tan 3x = 3 tanx
IIT study group
katieb
  • katieb
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anonymous
  • anonymous
@experimentX
experimentX
  • experimentX
tan 3x = ? ... expand this, solve the cubic or quartic equation for tan
anonymous
  • anonymous
Let me try by that way

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anonymous
  • anonymous
\[\tan 3x = \frac{ 3tanx - \tan^3 x }{ 1-3\tan^2x }\]
anonymous
  • anonymous
\[\frac{ 3\tan - \tan^3 x }{ 1-3 \tan^2 x } = 3tanx\] \[\tan^3 x = 9\tan^3 x\]
experimentX
  • experimentX
wolf says solution is n(pi) http://www.wolframalpha.com/input/?i=tan%283x%29+%3D+3+tan%28x%29
anonymous
  • anonymous
But hw...???
experimentX
  • experimentX
must be quartic in tan(x)
anonymous
  • anonymous
Nope...!
hartnn
  • hartnn
8 tan^3 x= 0 tan x = 0
experimentX
  • experimentX
tan(3x) = should have cubic ... you have only square ( quadratic)
hartnn
  • hartnn
tan x=0 only at n*pi
experimentX
  • experimentX
|dw:1352989835689:dw|
hartnn
  • hartnn
thats what he used.... tan^3 = 9 tan^3 so, 8tan^3= 0 --> tan x=0 which is true only for x=n*pi
experimentX
  • experimentX
|dw:1352990051780:dw|

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