Cos (3x-π/6)=cos ( x + π/4)

Question

Cos (3x-π/6)=cos ( x + π/4)

Answer 1

Cos(3x - π/6) - Cos(x + π/4) = 0  (применим формулу разности косинусов)
-2Sin(2x+π/12)*Sin(x - π/3) = 0
Sin(2x+π/12) = 0            или            Sin(x - π/3) = 0
2x + π/12 = πn , n ∈Z                        x - π/3 = πk, k ∈Z   
2x = nπ - π/12, n ∈Z                          x = πk + π/3, k ∈Z
x = nπ/2 - π/24 , n ∈Z