Решение
cos 2x/5-5sin x/5 +2=0
1 - 2sin² x/5 - 5sin x/5 + 2 = 0
2sin² x/5 + 5sin x/5 - 3 = 0
sin x/5 = t, I t I ≤ 1
2t² + 5t - 3 = 0
D = 25 + 4*2*3 = 49
t₁ = (- 5 - 7)/4
t₁ = - 3 не удовлетворяет условию I t I ≤ 1
t₂ = (- 5 + 7)/4
t₂ = 1/2
sin x/5 = 1/2
x/5= (-1)^n * arcsin(1/2) + πn, n ∈ Z
x/5= (-1)^n * (π/6) + πn, n ∈ Z
x = (-1)^n * (5π/6) + 5πn, n ∈ Z
Ответ: x = (-1)^n * (5π/6) + 5πn, n ∈ Z