Воспользуемся формулами:
cosα + cosβ = 2cos(α + β)/2 · cos(α - β)/2
cosα - cosβ = -2sin(α + β)/2 · sin(α - β)/2
Знаем: сos90° = 0, cos60° = 1/2, sin30° = 1/2
cos75° + cos15° = 2cos(75° + 15°)/2 · cos(75° - 15°) = 2cos90° · cos60° =
= 2 · 0 · 1/2 = 0
cos20° - cos80° = -2sin50° · sin(-30°) = 2sin50° · 1/2 = sin50°