sin(2x) - 3cos(x) = 0

2sin(x)cos(x) - 3cos(x) = 0

cos(x) • (2sin(x) - 3) = 0

[ cos(x) = 0

[ 2sin(x) - 3 = 0

<=>

[ x = π/2 + πn, n ∈ ℤ

[ sin(x) = 3/2

<=>

[ x = π/2 + πn, n ∈ ℤ

[ x = (-1)ⁿ • arcsin(3/2) + πn, n ∈ ℤ

Ответ:

x = π/2 + πn, n ∈ ℤ

x = (-1)ⁿ • arcsin(3/2) + πn, n ∈ ℤ