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I was thinking of sum of tangent.
$$ \tan 1^∘+ \tan 2^∘ + ... + \tan 89^∘= ? $$

I couldn't think of the answer of this. Wolfram Alpha didn't says the exact form of this answer.

Martin Sleziak
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buttercrab
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  • Are you sure that you have written down the problem correctly, and that it isn't $$\sum_{j=1}^{89} \tan(j)^2?$$ – Xander Henderson Nov 29 '17 at 14:46
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    Since possibly the correct statement is as mentioned by @XanderHenderson here is the duplicated post: https://math.stackexchange.com/questions/951522/trig-sum-tan-21-circ-tan-22-circ-tan2-89-circ?noredirect=1&lq=1 – Kal S. Nov 29 '17 at 14:50
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    By Riemann sums such expression is close to $$-\frac{180}{\pi}\log\sin\left(\frac{\pi}{360}\right).$$ Its actual numerical value is $\approx 265.017371462$. – Jack D'Aurizio Nov 29 '17 at 14:58

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