4 cos^3x=sin(х-3п/2) 

решить уравнение.

4 cos³x = sin(х-3π/2)

4 cos³x = -sin(3π/2 - х)

4 cos³x = сosх

cos²x = 1/4

1) cosx = 1/2

х₁ = ±π/3 + 2πn   n∈Z

2) cosx = -1/2

х₂ = ±2π/3 + 2πn   n∈Z