query: For any triangle $ABC$ what is the minimum value $\sum \frac{\sqrt{\sin A}}{\sqrt {\sin B}+\sqrt{\sin C}-\sqrt{\sin A}}$?
positive_passages.docid: 20055
positive_passages.text: Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$
negative_passages.docid: 32858
negative_passages.text: If a,b,c,d are positive integers with a sum of 63, what is the maximum value of ab + bc + cd ? (By using calculus to solve it))
negative_passages.docid: 216
negative_passages.text: In a $\triangle ABC,a^2+b^2+c^2=ac+ab\sqrt3$,then the triangle is
negative_passages.docid: 24221
negative_passages.text: Complex numbers - minimum value proof
negative_passages.docid: 62463
negative_passages.text: A pencil approach to find $\sum \limits_{i=1}^{69} \sqrt{\left( 1+\frac{1}{i^2}+\frac{1}{(i+1)^2}\right)}$
negative_passages.docid: 23694
negative_passages.text: Given that $abc=1$, prove that $\frac{b}{c} + \frac{c}{a}+ \frac{a}{b} \ge \frac{1}{a} + \frac{1}{b} +\frac{1}{c}$.
negative_passages.docid: 617
negative_passages.text: Find θ: $β=\arctan\frac{(R+r)·\sin(θ)-r·\sin(θ(1+\frac{R}{r}))}{(R+r)·\cos(θ)-r·\cos(θ(1+\frac{R}{r}))}$
negative_passages.docid: 34637
negative_passages.text: Evaluating $\sum\frac{\sin(n)}{n^a}$
negative_passages.docid: 9479
negative_passages.text: $\sum \cos$ when angles are in arithmetic progression
negative_passages.docid: 90030
negative_passages.text: What would be the value of $\sum\limits_{n=0}^\infty \frac{1}{an^2+bn+c}$
negative_passages.docid: 63071
negative_passages.text: the least possible value for :$ \lfloor \frac{a+b}{c}\rfloor +\lfloor \frac{b+c}{a} \rfloor+\lfloor \frac{c+a}{b} \rfloor $
negative_passages.docid: 55975
negative_passages.text: Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.
negative_passages.docid: 40779
negative_passages.text: What is the smallest possible value of $\lfloor (a+b+c)/d\rfloor+\lfloor (a+b+d)/c\rfloor+\lfloor (a+d+c)/b\rfloor+\lfloor (d+b+c)/a\rfloor$?
negative_passages.docid: 101476
negative_passages.text: If $A$, $B$ and $C$ are the angles of a triangle then find the value of $\Delta$
negative_passages.docid: 61302
negative_passages.text: Find the least value of $ \sec^6 x +\csc^6 x + \sec^6 x\csc^6 x$
negative_passages.docid: 115850
negative_passages.text: Minimum of $|ax-by+c|$
negative_passages.docid: 37744
negative_passages.text: Prove that given $a,b,c > 0$, it is possible to construct a triangle with sides of length $a,b,c$ if and only if $pa^2+qb^2 > pqc^2$