MathDB

1

Part of 1970 Poland - Second Round

Problems(1)

|cos nb- cos na| <= n^2 |cos b- cos a|,

Source: Polish MO second round 1970 p1

8/28/2024
Prove that ∣cos⁡nβ−cos⁡nα∣≤n2∣cos⁡β−cos⁡α∣, |\cos n\beta - \cos n\alpha| \leq n^2 |\cos \beta - \cos\alpha|, where nn is a natural number . Check for what values of n n , α \alpha , β \beta equality holds.
trigonometryinequalitiesalgebra