query: Beautiful sum of trigonometric roots
positive_passages.docid: 24222
positive_passages.text: Sum of the squares of the reciprocals of the fixed points of the tangent function
negative_passages.docid: 17188
negative_passages.text: Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer
negative_passages.docid: 95739
negative_passages.text: Sum of tangent functions where arguments are in specific arithmetic series
negative_passages.docid: 108461
negative_passages.text: Sum of Harmonic Numbers
negative_passages.docid: 83332
negative_passages.text: Trig sum: $\tan ^21^\circ+\tan ^22^\circ+\cdots+\tan^2 89^\circ = \text{?}$
negative_passages.docid: 44649
negative_passages.text: Summing a series having a geometric component
negative_passages.docid: 33396
negative_passages.text: Generalizing a Trig Identity
negative_passages.docid: 134633
negative_passages.text: How to sum this series for $\pi/2$ directly?
negative_passages.docid: 40952
negative_passages.text: Showing that sum of angles of hyperbolic triangle is strictly less than $\pi$
negative_passages.docid: 20713
negative_passages.text: The sum of an uncountable number of positive numbers
negative_passages.docid: 37855
negative_passages.text: Sums and harmonic series
negative_passages.docid: 94902
negative_passages.text: Simplifying a geometric sum
negative_passages.docid: 89561
negative_passages.text: Find the sum of angles without trigonometry?
negative_passages.docid: 117200
negative_passages.text: Evaluation of $ \sum_{k=0}^n \cos k\theta $
negative_passages.docid: 105238
negative_passages.text: Proving $\tan(\theta_1+\theta_2+\cdots+\theta_n)$ has the form $\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$
negative_passages.docid: 146047
negative_passages.text: Proving that $\cos(2\pi/n)$ is algebraic
negative_passages.docid: 69439
negative_passages.text: Infinite Sum of algebraic expression