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Yahoo!

Find the general solution of tan 3x = 3 tanx

  • one year ago
  • one year ago

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  1. Yahoo!
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    @experimentX

    • one year ago
  2. experimentX
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    tan 3x = ? ... expand this, solve the cubic or quartic equation for tan

    • one year ago
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    Let me try by that way

    • one year ago
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    \[\tan 3x = \frac{ 3tanx - \tan^3 x }{ 1-3\tan^2x }\]

    • one year ago
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    \[\frac{ 3\tan - \tan^3 x }{ 1-3 \tan^2 x } = 3tanx\] \[\tan^3 x = 9\tan^3 x\]

    • one year ago
  6. experimentX
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    wolf says solution is n(pi) http://www.wolframalpha.com/input/?i=tan%283x%29+%3D+3+tan%28x%29

    • one year ago
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    But hw...???

    • one year ago
  8. experimentX
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    must be quartic in tan(x)

    • one year ago
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    Nope...!

    • one year ago
  10. hartnn
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    8 tan^3 x= 0 tan x = 0

    • one year ago
  11. experimentX
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    tan(3x) = should have cubic ... you have only square ( quadratic)

    • one year ago
  12. hartnn
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    tan x=0 only at n*pi

    • one year ago
  13. experimentX
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    |dw:1352989835689:dw|

    • one year ago
  14. hartnn
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    thats what he used.... tan^3 = 9 tan^3 so, 8tan^3= 0 --> tan x=0 which is true only for x=n*pi

    • one year ago
  15. experimentX
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    |dw:1352990051780:dw|

    • one year ago
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