MathDB

Linear combinations of sin and cos

Source: Kvant Magazine No. 3 2020 M2594

March 10, 2023

algebratrigonometryKvant

Problem Statement

It is known that for some

x{}

and

y{}

the sums

\sin x+ \cos y

and

\sin y + \cos x

are positive rational numbers. Prove that there exist natural numbers

m{}

and

n{}

such that

m\sin x+n\cos x

is a natural number.
Proposed by N. Agakhanov