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Inverse trig problem - please help!

  1. Nov 15, 2013 #1
    Inverse trig problem -- please help!

    1. The problem statement, all variables and given/known data

    tanx+tan2x+root3tanxtan2x=root3
    find x........

    2. Relevant equations



    3. The attempt at a solution
    i have tried a lot and always ended with a complicated cubic equation...........
    please help me by giving me a another approach to the solution
     
  2. jcsd
  3. Nov 15, 2013 #2

    jedishrfu

    Staff: Mentor

    I'd try using the tan(a+b) identity to reduce the equation into terms with tan(x) factors.

    what is the root3 you mention? Is it some arbitrary constant?
     
  4. Nov 15, 2013 #3
    yes I have tried the same thing as you have said
    root3 is same as √3
     
  5. Nov 15, 2013 #4

    adjacent

    User Avatar
    Gold Member

    Do you mean:
    ##tan(x)+tan(2x)+\sqrt{3}*tan(x)*tan(2x)=\sqrt{3}## ?
     
  6. Nov 15, 2013 #5

    jedishrfu

    Staff: Mentor

    and you tried using the identity tan(2x) = 2tan(x) / (1-tan^2(x))

    and then collecting terms to create a cubic equation in tan(x) thats equal to zero.
     
  7. Nov 15, 2013 #6
  8. Nov 15, 2013 #7
    yes..
    how did you typed it??
     
  9. Nov 15, 2013 #8

    Mark44

    Staff: Mentor

    It is not enough to say what you have tried. You need to show us what you have tried.
     
  10. Nov 15, 2013 #9
    yes.... how did you typed it???
     
  11. Nov 15, 2013 #10
    i have used the identity of tan(A+B)
    then i simplified it and got a cubic equation in tanx
    and i dont know how to solve a cubic.........
    i am a high school student :)
     
  12. Nov 15, 2013 #11

    jedishrfu

    Staff: Mentor

    The PF website provides an advanced editor where you can enter mathematical expressions with subscripts, superscripts, summations, integrals...

    Use the "Go Advanced" button to the right of the "Post Quick Reply" button next time.
     
  13. Nov 15, 2013 #12

    adjacent

    User Avatar
    Gold Member

    Latex-Quote it and see how I've written it.You have to write
    Code (Text):
    ## and ##
    around the sentence.
     
  14. Nov 15, 2013 #13
    ok...:)
     
  15. Nov 15, 2013 #14

    jedishrfu

    Staff: Mentor


    So show us the cubic equation.

    The goal of the PF forum is help you with your homework not do it for you.
     
  16. Nov 15, 2013 #15

    ehild

    User Avatar
    Homework Helper
    Gold Member

    No need to solve a cubic equation.
    Notice that √3=tan(π/3)

    You can rearrange the equation as

    [tex]\tan(2x)(1+\sqrt3 \tan(x))=\sqrt3 - \tan(x) [/tex]

    that is

    [tex]\tan(2x)=\frac{\sqrt3 - \tan(x)}{1+\sqrt3 \tan(x)} [/tex]

    Recall that

    [tex]\tan(a-b)=\frac{\tan(a) - \tan(b)}{1+\tan(a) \tan(b)} [/tex]



    ehild
     
  17. Nov 15, 2013 #16
    i have got this equation
    (tanx)3-3[itex]\sqrt{}3[/itex](tanx)2-3tanx+[itex]\sqrt{}3[/itex] =0
     
  18. Nov 15, 2013 #17
    thanks.......!!
     
  19. Nov 15, 2013 #18

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You are welcome:smile:


    ehild
     
  20. Nov 15, 2013 #19

    jedishrfu

    Staff: Mentor

    dont forget to thank ehild via the thanks button.
     
  21. Nov 15, 2013 #20

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It had been done and very properly:biggrin:

    ehild
     
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