MathDB

5

Part of 1968 Swedish Mathematical Competition

Problems(1)

min value of (cos ax + cos bx) <= r < 0

Source: 1968 Swedish Mathematical Competition p5

3/21/2021
Let a,ba, b be non-zero integers. Let m(a,b)m(a, b) be the smallest value of cos⁡ax+cos⁡bx\cos ax + \cos bx (for real xx). Show that for some rr, m(a,b)≤r<0m(a, b) \le r < 0 for all a,ba, b.
trigonometryalgebramininequalities