2cos^3 x+1=cos^2(3pi/2-x)

2cos³x +1 = cos²(3π/2 -x) ;2cos³x +1 = sin²x ;2cos³x +(1 -  sin²x ) =0 ;2cos³x +cos²x =0 ;2cos²x(cosx +1/2) =0 ;[ cosx =0 ; cosx = -1/2.⇔[ x=π/2 +π*k ;k∈Z  ;a) cosx =0⇒ x =π/2 +π*k , k∈Z.b) cosx = - 1/2 ⇒x = ±2π/3 +2π*k, k∈Z.