query: Question about the minimum value of $2^{\sin^2a}+2^{\cos^2a}$.
positive_passages.docid: 140001
positive_passages.text: Minimum value of $2^{\sin^2x}+2^{\cos^2x}$
negative_passages.docid: 38702
negative_passages.text: How to minimize $|z_1 - z_2|^2 + |z_1 - z_4|^2 + |z_2 - z_3|^2 + |z_3 - z_4|^2$?
negative_passages.docid: 52018
negative_passages.text: Can $\frac{\sqrt{3}}{\sin20^{\circ}}-\frac{1}{\cos20^{\circ}}$ have two values?
negative_passages.docid: 106803
negative_passages.text: How to see $\cos x \leq \exp(-x^2/2)$ on $x \in [0,\pi/2]$?
negative_passages.docid: 75349
negative_passages.text: Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$
negative_passages.docid: 144859
negative_passages.text: Finding parameters for $f(x) = x^2 + 2(m − a)x + 3am −2 = 0$ that satisfy a condition.
negative_passages.docid: 48154
negative_passages.text: Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.
negative_passages.docid: 57736
negative_passages.text: Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$
negative_passages.docid: 23638
negative_passages.text: $a^2b^2+a^2c^2+b^2c^2\leq 3$
negative_passages.docid: 122705
negative_passages.text: Solution of trigonometric equation $0 = x\cos(x)+2$
negative_passages.docid: 107067
negative_passages.text: Finding the argument of $z=1-\cos(2\theta)-i\sin(2\theta)$
negative_passages.docid: 115850
negative_passages.text: Minimum of $|ax-by+c|$
negative_passages.docid: 45343
negative_passages.text: Solve $\cos^{n}x-\sin^{n}x=1$ with $n\in \mathbb{N}$.
negative_passages.docid: 143070
negative_passages.text: If $\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$ then $x^2 - 44x - 36 = 0$ holds for $x=\sin 2A$
negative_passages.docid: 88432
negative_passages.text: A problem on range of a trigonometric function: what is the range of $\frac{\sqrt{3}\sin x}{2+\cos x}$?
negative_passages.docid: 29424
negative_passages.text: Maximum value of $\sin A+\sin B+\sin C$?
negative_passages.docid: 38254
negative_passages.text: Trigonometry Olympiad problem: Evaluate $1\sin 2^{\circ} +2\sin 4^{\circ} + 3\sin 6^{\circ}+\cdots+ 90\sin180^{\circ}$