Quote:
Originally Posted by alpertron
It appears that you typed extra end of line characters inside the identities. After deleting these, we can see the formulas

Hmm, must be a difference in display settings, the two look exactly the same to me!
In any event, a theoretically more satisfactory approach, applicable to dividing an angle by any positive integer, is to use the multipleangle formulas to get a polynomial equation for the required trig function. In the case of the tangent, let t = tan(\theta). Then, for k a positive integer,
may be expressed as Im(1+i*t)^k/Re(1 + i*t)^k. Setting this rational expression equal to a given value for
gives a polynomial for t =
. The zeroes of the polynomial are
, j = 0 to k1.
In the case k = 2, the rational expression is 2t/(1  t^2).