Question

What is the exact value of $\frac{1}{\tan20^{\circ}}-\frac{1}{\sin80^{\circ}}$?

score 297 · Answer 1 · 2017-02-25 08:26:53

297

Views

What is the exact value of $\frac{1}{\tan20^{\circ}}-\frac{1}{\sin80^{\circ}}$?

Published on 25 Feb 2017 - 8:26

score 77 · Answer 2 · 2017-02-25 11:51:31

77

Views

Prove equivalent fractions with $\pm$ sign

Published on 25 Feb 2017 - 11:51

score 69 · Answer 3 · 2026-03-30 09:38:40

69

Views

Limit of a sequence of fractions

Published on 30 Mar 2026 - 9:38

score 173 · Answer 4 · 2017-02-26 17:50:46

173

Views

What is the mean of these twelve mixed numbers?

Published on 26 Feb 2017 - 17:50

score 84 · Answer 5 · 2026-03-28 13:29:46

84

Views

Exponent Simplification

Published on 28 Mar 2026 - 13:29

score 175 · Answer 6 · 2017-02-28 12:27:34

175

Views

Kids on a $45$-seat bus

Published on 28 Feb 2017 - 12:27

score 180 · Answer 7 · 2026-03-28 15:26:31

180

Views

Inequality involving sum with parameter in denominator (leading to harmonic number problem)

Published on 28 Mar 2026 - 15:26

score 180 · Answer 8 · 2017-03-02 06:10:35

180

Views

For $a,b,c<1$. Minimize $M=\frac{a^2\left(1-2b\right)}{b}+\frac{b^2\left(1-2c\right)}{c}+\frac{c^2\left(1-2a\right)}{a}$

Published on 02 Mar 2017 - 6:10

score 240 · Answer 9 · 2026-03-25 22:05:32

240

Views

Prove that $\frac{1}{\left(2a+b\right)^2}+\frac{1}{\left(2b+c\right)^2}+\frac{1}{\left(2c+a\right)^2}\ge\frac{1}{ab+bc+ca}$

Published on 25 Mar 2026 - 22:05

score 119 · Answer 10 · 2026-03-25 09:29:17

119

Views

Prove that $\frac{(2a+b+c)^2}{2a^2+(b+c)^2}+\frac{(2b+c+a)^2}{2b^2+(c+a)^2}+\frac{(2c+a+b)^2}{2c^2+(a+b)^2} \le 8$

Published on 25 Mar 2026 - 9:29

score 52 · Answer 11 · 2017-03-04 14:05:28

52

Views

Help to simplify this complicated fraction

Published on 04 Mar 2017 - 14:05

score 4.2k · Answer 12 · 2017-03-06 13:51:53

4.2k

Views

Can a negative number be raised to a fractional power e.g $2.5$?

Published on 06 Mar 2017 - 13:51

score 50 · Answer 13 · 2017-03-06 21:02:19

50

Views

Show that $\frac 1x+\frac 1y =(\frac 27)^a$ does not produce integer solutions for $a > 3$.

Published on 06 Mar 2017 - 21:02

score 112 · Answer 14 · 2026-03-30 15:45:03

112

Views

For $a,b,c>0$ prove that $\frac{a}{a+\sqrt{(a+b)(a+c)}} + \frac{b}{b+\sqrt{(b+a)(b+c)}}+ \frac{c}{c+\sqrt{(c+b)(c+a)}} \leq 1$

Published on 30 Mar 2026 - 15:45

score 271 · Answer 15 · 2026-03-29 10:49:06

271

Views

For $a,b,c$. Prove that $\frac{a^2}{a+\sqrt[3]{bc}}+\frac{b^2}{b+\sqrt[3]{ca}}+\frac{c^2}{c+\sqrt[3]{ab}}\ge\frac{3}{2}$

Published on 29 Mar 2026 - 10:49

List Question

What is the exact value of $\frac{1}{\tan20^{\circ}}-\frac{1}{\sin80^{\circ}}$?

Prove equivalent fractions with $\pm$ sign

Limit of a sequence of fractions

What is the mean of these twelve mixed numbers?

Exponent Simplification

Kids on a $45$-seat bus

Inequality involving sum with parameter in denominator (leading to harmonic number problem)

For $a,b,c<1$. Minimize $M=\frac{a^2\left(1-2b\right)}{b}+\frac{b^2\left(1-2c\right)}{c}+\frac{c^2\left(1-2a\right)}{a}$

Prove that $\frac{1}{\left(2a+b\right)^2}+\frac{1}{\left(2b+c\right)^2}+\frac{1}{\left(2c+a\right)^2}\ge\frac{1}{ab+bc+ca}$

Prove that $\frac{(2a+b+c)^2}{2a^2+(b+c)^2}+\frac{(2b+c+a)^2}{2b^2+(c+a)^2}+\frac{(2c+a+b)^2}{2c^2+(a+b)^2} \le 8$

Help to simplify this complicated fraction

Can a negative number be raised to a fractional power e.g $2.5$?

Show that $\frac 1x+\frac 1y =(\frac 27)^a$ does not produce integer solutions for $a > 3$.

For $a,b,c>0$ prove that $\frac{a}{a+\sqrt{(a+b)(a+c)}} + \frac{b}{b+\sqrt{(b+a)(b+c)}}+ \frac{c}{c+\sqrt{(c+b)(c+a)}} \leq 1$

For $a,b,c$. Prove that $\frac{a^2}{a+\sqrt[3]{bc}}+\frac{b^2}{b+\sqrt[3]{ca}}+\frac{c^2}{c+\sqrt[3]{ab}}\ge\frac{3}{2}$

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