query: Simplify $\cos 1^\circ + \cos 3^\circ + \cdots+ \cos 43^\circ$?
positive_passages.docid: 9479
positive_passages.text: $\sum \cos$ when angles are in arithmetic progression
negative_passages.docid: 14386
negative_passages.text: Proof of an equality involving cosine $\sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{2}}}}\ =\ 2\cos (\pi/2^{n+1})$
negative_passages.docid: 104384
negative_passages.text: Trigonometric identity: $\frac {\tan\theta}{1-\cot\theta}+\frac {\cot\theta}{1-\tan\theta} =1+\sec\theta\cdot\csc\theta$
negative_passages.docid: 10222
negative_passages.text: Simplify $\sum (x_i- \mu)^2$
negative_passages.docid: 12414
negative_passages.text: prove that : $\cos x \cdot \cos(x-60^{\circ}) \cdot \cos(x+60^{\circ})= \frac14 \cos3x$
negative_passages.docid: 149675
negative_passages.text: Simplifying $\sqrt[4]{161-72 \sqrt{5}}$
negative_passages.docid: 100971
negative_passages.text: How to simplify the series of $x + x^{-1} + (x + x^{-1})^{-1} + (x + x^{-1} + (x + x^{-1})^{-1})^{-1}$?
negative_passages.docid: 36951
negative_passages.text: How to evaluate the series $1+\frac34+\frac{3\cdot5}{4\cdot8}+\frac{3\cdot5\cdot7}{4\cdot8\cdot12}+\cdots$
negative_passages.docid: 30851
negative_passages.text: Find the summation $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \cdots$
negative_passages.docid: 58633
negative_passages.text: Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
negative_passages.docid: 151085
negative_passages.text: Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
negative_passages.docid: 38254
negative_passages.text: Trigonometry Olympiad problem: Evaluate $1\sin 2^{\circ} +2\sin 4^{\circ} + 3\sin 6^{\circ}+\cdots+ 90\sin180^{\circ}$
negative_passages.docid: 76282
negative_passages.text: Prime number expressible as $2^2+3^3+5^5+7^7+11^{11}+\cdots$
negative_passages.docid: 89319
negative_passages.text: How can I find all the solutions of $\sin^5x+\cos^3x=1$
negative_passages.docid: 118408
negative_passages.text: Equation with cos and product
negative_passages.docid: 142610
negative_passages.text: Solving $\sin x\cos3x+\cos x\sin3x=\sqrt{3}/2$ in the interval $[0,2\pi]$
negative_passages.docid: 16866
negative_passages.text: How to Prove $a^3 \cos (B-C) + b^3 \cos (C-A)+ c^3 \cos (A-B)=3abc$?