benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Does there exist an angle α∈(0,π/2) such that sinα, cosα, tanα and cotalpha, taken in some order, are consecutive terms of an arithmetic progression?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Does there exist an angle α∈(0,π/2) \alpha\in(0,\pi/2) such that sinα \sin\alpha, cosα \cos\alpha, tanα \tan\alpha and $ \cot\alpha$, taken in some order, are consecutive terms of an arithmetic progression?
Plain-text mathematical notation (without MathML)
Does there exist an angle α∈(0,π/2) such that sinα, cosα, tanα and $ \cot\alpha$, taken in some order, are consecutive terms of an arithmetic progression?
Original LaTeX notation
Does there exist an angle $ \alpha\in(0,\pi/2)$ such that $ \sin\alpha$, $ \cos\alpha$, $ \tan\alpha$ and $ \cot\alpha$, taken in some order, are consecutive terms of an arithmetic progression?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
c9f22746-e8cb-5146-a780-dd9a01e9a4f4
task_key
test--c9f22746-e8cb-5146-a780-dd9a01e9a4f4
task_revision_id
1
config / split
/ test

Official source

initial import