query: Proving that $\cot^220^\circ + \cot^240^\circ + \cot^280^\circ = 9$.
positive_passages.docid: 142673
positive_passages.text: Evaluate $\tan^{2}(20^{\circ}) + \tan^{2}(40^{\circ}) + \tan^{2}(80^{\circ})$
negative_passages.docid: 128415
negative_passages.text: Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots+\frac{1}{3001}<\frac43$
negative_passages.docid: 60122
negative_passages.text: Prove $(1+a+b)(1+b+c)(1+c+a)\ge 9(ab+bc+ca)$
negative_passages.docid: 281
negative_passages.text: How one can prove $\prod_{k=1}^{n-1} (\cos\theta-\cos(k\pi/n)) = 2^{1-n}\sin(n\theta)\csc\theta$?
negative_passages.docid: 98745
negative_passages.text: To prove $(\sin\theta + \csc\theta)^2 + (\cos\theta +\sec\theta)^2 \ge 9$
negative_passages.docid: 11711
negative_passages.text: Prove trigonometry identity for $\cos A+\cos B+\cos C$
negative_passages.docid: 112237
negative_passages.text: prove this :$\sum_1^{100} A_i = \sum_0^{99} C_i $
negative_passages.docid: 48824
negative_passages.text: Prove: $ \frac{1}{\sin 2x} + \frac{1}{\sin 4x } + \cdots + \frac{1 }{\sin 2^n x} = \cot x - \cot 2^n x $
negative_passages.docid: 122878
negative_passages.text: How can I prove that $2/9<x^4+y^4<8$?
negative_passages.docid: 95061
negative_passages.text: Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
negative_passages.docid: 85872
negative_passages.text: Prove $1 + \tan^2\theta = \sec^2\theta$
negative_passages.docid: 2019
negative_passages.text: Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$
negative_passages.docid: 67666
negative_passages.text: show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
negative_passages.docid: 133819
negative_passages.text: How to prove that $364 \mid n^{91} - n^7$?
negative_passages.docid: 141909
negative_passages.text: Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
negative_passages.docid: 146053
negative_passages.text: Proving identities (mod $pq$) using Fermat's little theorem?
negative_passages.docid: 14386
negative_passages.text: Proof of an equality involving cosine $\sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{2}}}}\ =\ 2\cos (\pi/2^{n+1})$