Trigonometric Identity Similar to Tangent Addition Identity

Question

I found the following trigonometric relationship in a paper and I can't seem to derive it.

$1/2 arctan(\frac{2\sqrt{l}}{l-1}) = arctan(\sqrt{l})$

Where $l$ is a natural number. It seems similar to the tangent addition identity, but I can't use this identity to make a connection between the two.

score 0 · Answer 1 · edited Apr 13 '17 at 12:20

0

$$2\arctan\sqrt l=\arctan\dfrac{2\sqrt l}{1-l}\text{ if }\sqrt l<1$$

edited Apr 13 '17 at 12:20

Community

answered Apr 20 '16 at 05:26

lab bhattacharjee

\sqrt{l}<1 doesn't hold for my problem. – billbob Apr 20 '16 at 05:40
@billbob, Why & where it is specified? – lab bhattacharjee Apr 20 '16 at 05:41
In the question. I say $l$ is a natural, but make no mention of the assumption you make, so you should assume that it doesn't hold. – billbob Apr 20 '16 at 05:46
@billbob, Can be $l=0?$ Then we have three cases $l=0,1,>1$ – lab bhattacharjee Apr 20 '16 at 05:49
@billbob, "Regrettably, there seems to be no general agreement about whether to include 0 in the set of natural numbers." : http://mathworld.wolfram.com/NaturalNumber.html – lab bhattacharjee Apr 20 '16 at 05:50
Right, $l \ge 1$ – billbob Apr 20 '16 at 05:59

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