Rational trig identities?
10-10-2021, 04:42 PM
Post: #1
 John Keith Senior Member Posts: 864 Joined: Dec 2013
Rational trig identities?
Surprisingly (to me), tan(n * arctan(1/n)) is rational when n is an integer. However, I can't get Mathematica nor the Prime CAS nor the 50g in exact mode to express this formula as a rational expression. Am I missing something obvious (probably!) or are such simplifications beyond the abilities of CAS's?

An iterative program is shown at A348140 but no formula is given. Here is a translation for the 49g/50g (exact mode):

Code:
 \<< DUP INV \-> n s   \<< s 1 n  1 -     START DUP s + SWAP n / 1 SWAP - / EVAL     NEXT   \>> \>>
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 Messages In This Thread Rational trig identities? - John Keith - 10-10-2021 04:42 PM RE: Rational trig identities? - Albert Chan - 10-10-2021, 06:21 PM RE: Rational trig identities? - Albert Chan - 10-10-2021, 08:02 PM RE: Rational trig identities? - Albert Chan - 10-12-2021, 04:05 PM RE: Rational trig identities? - Albert Chan - 10-10-2021, 09:25 PM RE: Rational trig identities? - John Keith - 10-11-2021, 01:08 PM RE: Rational trig identities? - Albert Chan - 10-12-2021, 02:09 PM

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