Value of a series in $\tan$

Question

Question: The value of: $$(1+\tan 1^o)(1+\tan 2^o)(1+\tan 3^o)...(1+\tan 44^o)$$ is:

A) 2

B) A multiple of 22

C) A multiple of 4

D) Not an integer

I'm not sure how I would solve this question. However, by intuition, I would say that the number wouldn't be an integer. As all the terms in the bracket are between 1 and 2, their product shouldn't give an integral value. Am I right?

See http://math.stackexchange.com/questions/304461/x-1-tan-1-circ1-tan-2-circ1-tan-3-circ-ldots1-tan?rq=1 — lab bhattacharjee, May 07 '16 at 07:24
$\frac 32$ and $\frac 43$ are between $1$ and $2$ too -- do you contend their product is not an integer? — hmakholm left over Monica, May 07 '16 at 07:37
@HenningMakholm Aha.... Don't know how I missed that. Thanks anyways I have checked the similar questions :) — Gummy bears, May 07 '16 at 07:42

score 1 · Answer 1 · answered May 07 '16 at 07:52

1

Note I found something interesting $(1+tan(1degree))(1+tan(44degree))\approx 2$ this can easily be proved by simplifying $(1+tan(a))(1+tan(45-a))$

answered May 07 '16 at 07:52

Archis Welankar

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Value of a series in $\tan$

1 Answers1