Due to a result from Chowla, we know that the set $\cot(2\pi k/n)$, such that $\gcd(k, n) = 1$, is linearly independent over the Rationals.
Do we have any similar results for $\sec^2(2\pi k/n)$ or $\tan^2(2\pi k/n)$ ?
Thanks
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$\begingroup$ Perhaps you just need to use common trig identities to answer this. $\endgroup$– SquirtleAug 5, 2014 at 0:41
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$\begingroup$ I don't get it...how do I use common trig identities to solve answer this? $\endgroup$– MikeAug 5, 2014 at 10:38
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1 Answer
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K. Wang, On a theorem of S. Chowla, J. Number of theory 15 (1982), 1-4 all the derivatives of cot(x) which includes sec-squared and hence tan-sqared.
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$\begingroup$ okada, on an extension of a theorem of S Chowla $\endgroup$– kai wangJun 24, 2016 at 17:23