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Recurrence relation of tangent

  1. Jan 17, 2010 #1
    Is it possible to find a recurrence relation of tan(nx) where n is a positive integer and x is a real variable?

    My friend said that it is possible.

    I don't see how to do it.

    Does anyone have a way to do it?
     
  2. jcsd
  3. Jan 17, 2010 #2

    HallsofIvy

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    Science Advisor

    You should know the sum formula tan(A+ B)= (tan(A)+ tan(B))/(1+ tan(A)(tan(B)).

    Using that, tan((n+1)x)= tan(x+ nx= (tan(x)+ tan(nx))/(1+ tan(x)tan(nx))
    or, if we write Tn= tan(nx),

    Tn+1= (T_1+ T_n)/(1+ T_1T_n), a recurrance relation.
     
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