query: Trigonometric Ratios with half angles
positive_passages.docid: 147684
positive_passages.text: Prove that $\sin \theta=\frac{3 \sin \alpha+\sin^3 \alpha}{1+3\sin^2 \alpha}$ using given condition
negative_passages.docid: 58932
negative_passages.text: Hard contest type trigonometry proof
negative_passages.docid: 120148
negative_passages.text: prove this properties of triangles trigonometric question
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: 95633
negative_passages.text: Help with this trigonometry problem
negative_passages.docid: 96065
negative_passages.text: Question about sines of angles in an acute triangle
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: 66872
negative_passages.text: Exact values of $\cos(2\pi/7)$ and $\sin(2\pi/7)$
negative_passages.docid: 128006
negative_passages.text: How to get ratio of a,b,c from 2 equations in a,b,c
negative_passages.docid: 61343
negative_passages.text: Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
negative_passages.docid: 12646
negative_passages.text: In acute angle triangle, prove that $\cos (A-B) \cos (B-C) \cos (C-A)\ge 8\cos A \cos B \cos C$
negative_passages.docid: 51979
negative_passages.text: Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$?
negative_passages.docid: 56934
negative_passages.text: How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ ?.
negative_passages.docid: 145559
negative_passages.text: Trigonometry problem on product of trig functions.
negative_passages.docid: 89003
negative_passages.text: Finding a trigonometric polynomial
negative_passages.docid: 90708
negative_passages.text: Comparing angles and working out the difference
negative_passages.docid: 33100
negative_passages.text: Trigonomnetric equality involving tg