Решение
2cosx*cos2x=cosx
2cosx*cos2x - cosx = 0
cosx*(2cos2x - 1) = 0
1) cosx = 0
x₁ = π/2 + πk, k ∈ Z
2) 2cos2x - 1 = 0
cos2x = 1/2
2x = (+ -)arccos(1/2) + 2πn, n ∈ Z
2x = (+ -)*(π/3) + 2πn, n ∈ Z
x₂ = (+ -)*(π/6) + πn, n ∈ Z
Ответ: x₁ = π/2 + πk, k ∈ Z ; x₂ = (+ -)*(π/6) + πn, n ∈ Z