Trigonometry: arctan equation?

  • Thread starter XYZ313
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  • #1
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Can someone please let me know how to find x in

π/4=arctan(x+arctan(x+...)) ?
 

Answers and Replies

  • #2
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Let me do a similar one:

Let [itex]x=\sqrt{2+\sqrt{2+\sqrt{2+...}}}[/itex]. Then [itex]x^2-2=x[/itex].
Solving the quadratic equation gives us the answer.

Can you do your problem now along similar lines??
 
  • #3
21
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micromass: isn't it the use of inverse operator (tan in this case)?
like z=arctan(x+arctan(x+...)) and make the use of tanz?

and then use tan addition rule??? I am really confused...

Can you explain further please?
 
  • #4
lurflurf
Homework Helper
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π/4=arctan(x+arctan(x+...))
take tan of both sides
tan(π/4)=tan(arctan(x+arctan(x+...)) )
 
  • #5
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lurflurf: and then what?

tan(π/4) = x + arctan(x+arctan(x+...)) ???
 
  • #6
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what is tan(tanx)??? Is above equation some kind of sum of geometric progress???
 
  • #7
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is it so easy that no one is going even to comment?
 
  • #8
lurflurf
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tan(π/4)=tan(arctan(x+arctan(x+...)) )
1=x+arctan(x+arctan(x+...))
 
  • #9
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lurflurf: thank you, this is obvious and not the solution

then

tan(1-x) = x + arctan(x+arctan(x+...))

and where it is leading???
 
  • #10
lurflurf
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arctan(x+arctan(x+...)) ?
 
  • #11
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if I knew what "arctan(x+arctan(x+...))" equals to, I wouldn't be posting this thread...
 
  • #12
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if I knew what "arctan(x+arctan(x+...))" equals to, I wouldn't be posting this thread...
What? You said what this equals in your first post. It's x that is the unknown.
 
  • #13
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spamiam: right, sorry, I'm really dumb

x = 1 - π/4

Thank you all for bearing with me...
 
  • #14
21
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This is dumbest question I have ever asked. Hope this is never going to happen again...
 
  • #15
360
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You're not dumb--this question is difficult until you see the trick to use.
 

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