Решить уравнение cos (3x + П/6) + cos (x + П/4) = 0

Сos (3x + π/6) + Сos (x + π / 4) = 0

есть формула: Cos α + Cosβ = 2Sin (α+β) / 2 * Sin (α-β) / 2

применим её:

2Sin (3x + π/6 + x + π/4) / 2 * Sin ((3x + π/6 - x - π/4) / 2 = 0

2Sin (2x + 5π/24) * Sin (x - π/24) = 0

Sin (2x + 5π/24) = 0 или Sin (x - π/24) = 0

2 х + 5π/24 = πn, n ∈Z x - π/24 = πm, m ∈Z

2x = πn - 5π/24, n ∈ Z x = πm + π/24, m ∈Z

x = πn/2 - 5π/48, n ∈Z