Question

How to prove $t+\sum\limits_{n=1}^{t-1} 2(t-n)\cos(nx) = \frac{1-\cos(tx)}{1-\cos(x)}$

score 78 · Answer 1 · 2026-04-15 18:39:11

78

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How to prove $t+\sum\limits_{n=1}^{t-1} 2(t-n)\cos(nx) = \frac{1-\cos(tx)}{1-\cos(x)}$

Published on 15 Apr 2026 - 18:39

score 173 · Answer 2 · 2026-04-17 05:04:12

173

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If $\cos x=\cos y$ and $\sin x=\sin y$ is $x=y$ or $x=2\pi,y=0$ or $x=0,y=2\pi$? $x,y\in[0,2\pi]$

Published on 17 Apr 2026 - 5:04

score 123 · Answer 3 · 2026-04-16 12:31:16

123

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$\cos(x)\cos(mx)$ is a polynomial in $\sin(x)^{2}$ with degree $\le (m-1)/2$

Published on 16 Apr 2026 - 12:31

score 105 · Answer 4 · 2026-04-15 22:33:56

105

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Inequality in triangle: $2\cos(A)\le\cos(B-C)$

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score 74 · Answer 5 · 2026-04-16 13:50:30

74

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How to find the radius of the circle after adding the area of segment?

Published on 16 Apr 2026 - 13:50

score 453 · Answer 6 · 2026-04-11 11:02:08

453

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Related Rates change in theta

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score 642 · Answer 7 · 2026-04-15 21:23:32

642

Views

Continuous function and limit $ f(x,y)=\left\{\begin{matrix} (x-y)\sin\frac{1}{x}\sin\frac{1}{y} & , xy\neq 0 \\ 0 &, x=y=0 \end{matrix}\right. $

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score 914 · Answer 8 · 2026-04-12 02:00:53

914

Views

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score 90 · Answer 9 · 2026-04-11 00:34:10

90

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Solve the equation $R^{2}\frac{\arccos(\frac{h}{R})+\frac{h}{R}}{2} = \pi r^{2}$ for $R$

Published on 11 Apr 2026 - 0:34

score 95 · Answer 10 · 2026-04-16 14:49:05

95

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When is $2\cos(\pi \frac{i}{n}) + 2\cos(\pi \frac{j}{m}) = -1 $

Published on 16 Apr 2026 - 14:49

score 427 · Answer 11 · 2026-04-09 21:23:29

427

Views

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score 221 · Answer 12 · 2026-04-16 19:04:06

221

Views

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Published on 16 Apr 2026 - 19:04

score 37 · Answer 13 · 2026-04-08 18:25:56

37

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score 49 · Answer 14 · 2026-04-13 15:49:05

49

Views

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Published on 13 Apr 2026 - 15:49

score 507 · Answer 15 · 2026-04-11 05:16:06

507

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A peculiar integral identity

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List Question

How to prove $t+\sum\limits_{n=1}^{t-1} 2(t-n)\cos(nx) = \frac{1-\cos(tx)}{1-\cos(x)}$

If $\cos x=\cos y$ and $\sin x=\sin y$ is $x=y$ or $x=2\pi,y=0$ or $x=0,y=2\pi$? $x,y\in[0,2\pi]$

$\cos(x)\cos(mx)$ is a polynomial in $\sin(x)^{2}$ with degree $\le (m-1)/2$

Inequality in triangle: $2\cos(A)\le\cos(B-C)$

How to find the radius of the circle after adding the area of segment?

Related Rates change in theta

Continuous function and limit $ f(x,y)=\left\{\begin{matrix} (x-y)\sin\frac{1}{x}\sin\frac{1}{y} & , xy\neq 0 \\ 0 &, x=y=0 \end{matrix}\right. $

Calculating Hyperbolic Sin faster than using a standard power series

Solve the equation $R^{2}\frac{\arccos(\frac{h}{R})+\frac{h}{R}}{2} = \pi r^{2}$ for $R$

When is $2\cos(\pi \frac{i}{n}) + 2\cos(\pi \frac{j}{m}) = -1 $

Finding specific solutions to trigonometric equations

Showing that $\arctan x = \arcsin\left(\frac{x}{\sqrt{1 + x^2}}\right)$

How to change a sine function?

Any fun way applying concepts at home

A peculiar integral identity

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