Question

Showing that $\cos^p{\Theta} \le \cos{p\Theta}$, for $0<\Theta<\frac{\pi}{2}$ and $0<p<1$, by analyzing $f(\theta)=\frac{\cos^p\Theta}{\cos p\Theta}$

score 342 · Answer 1 · 2026-04-19 17:40:57

Showing that $\cos^p{\Theta} \le \cos{p\Theta}$, for $0<\Theta<\frac{\pi}{2}$ and $0<p<1$, by analyzing $f(\theta)=\frac{\cos^p\Theta}{\cos p\Theta}$

score 664 · Answer 2 · 2026-04-11 20:28:44

664

Views

Proving $|CH| = 2|OM|$ of $\triangle ABC$ of which $O$ is the circumcenter and $H$ is the orthocenter.

Published on 11 Apr 2026 - 20:28

score 48 · Answer 3 · 2026-04-12 14:14:20

48

Views

Equivalent condition to the existence of a limit, help understanding proof

Published on 12 Apr 2026 - 14:14

score 357 · Answer 4 · 2026-04-29 03:23:13

357

Views

In a given vector space V the zero vector is unique

Published on 29 Apr 2026 - 3:23

score 382 · Answer 5 · 2026-04-12 04:00:04

382

Views

$U\times W \cong V\times W $ does this imply that $U\cong V$

Published on 12 Apr 2026 - 4:00

score 408 · Answer 6 · 2026-04-14 05:16:42

408

Views

Proof that the Sum of Products is Zero

Published on 14 Apr 2026 - 5:16

score 30 · Answer 7 · 2026-04-11 00:08:56

30

Views

Proof verification for bounded sets.

Published on 11 Apr 2026 - 0:08

score 63 · Answer 8 · 2026-04-14 19:35:07

63

Views

For all $0<a\in \Bbb R$, there exists a unique $0<x\in \Bbb R$ such that $x^2=a$

Published on 14 Apr 2026 - 19:35

score 153 · Answer 9 · 2026-04-08 18:38:21

153

Views

An attempted proof of Cauchy's theorem for abelian groups using composition series.

Published on 08 Apr 2026 - 18:38

score 275 · Answer 10 · 2026-04-16 07:34:18

275

Views

Thm: If n is an odd pseudo prime number, then $M_n = 2^n-1$ is a larger one.

Published on 16 Apr 2026 - 7:34

score 178 · Answer 11 · 2026-04-13 14:03:42

178

Views

Alternative approaches to obtain the expected value of the geometric distribution

Published on 13 Apr 2026 - 14:03

score 66 · Answer 12 · 2026-04-13 18:35:52

66

Views

Given $B \subseteq A$ and $x \in A$, x could also be in B

Published on 13 Apr 2026 - 18:35

score 50 · Answer 13 · 2026-04-15 19:35:22

Showing there exists no sequence of indicator functions on $\mathbb{R}^\mathbb{R}$ that converges to the indicator function on $\mathbb{R}$

score 329 · Answer 14 · 2026-04-14 18:09:06

329

Views

Is it true that x in base n is always larger than or equal to x in base n-1?

Published on 14 Apr 2026 - 18:09

score 195 · Answer 15 · 2026-04-14 14:54:31

195

Views

Conditional probability and binomial distributions: am I doing it right?

Published on 14 Apr 2026 - 14:54

List Question

Showing that $\cos^p{\Theta} \le \cos{p\Theta}$, for $0<\Theta<\frac{\pi}{2}$ and $0<p<1$, by analyzing $f(\theta)=\frac{\cos^p\Theta}{\cos p\Theta}$

Proving $|CH| = 2|OM|$ of $\triangle ABC$ of which $O$ is the circumcenter and $H$ is the orthocenter.

Equivalent condition to the existence of a limit, help understanding proof

In a given vector space V the zero vector is unique

$U\times W \cong V\times W $ does this imply that $U\cong V$

Proof that the Sum of Products is Zero

Proof verification for bounded sets.

For all $0<a\in \Bbb R$, there exists a unique $0<x\in \Bbb R$ such that $x^2=a$

An attempted proof of Cauchy's theorem for abelian groups using composition series.

Thm: If n is an odd pseudo prime number, then $M_n = 2^n-1$ is a larger one.

Alternative approaches to obtain the expected value of the geometric distribution

Given $B \subseteq A$ and $x \in A$, x could also be in B

Showing there exists no sequence of indicator functions on $\mathbb{R}^\mathbb{R}$ that converges to the indicator function on $\mathbb{R}$

Is it true that x in base n is always larger than or equal to x in base n-1?

Conditional probability and binomial distributions: am I doing it right?

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