4cos^3x-4cos^2x+cosx-1=0

Question

4cos^3x-4cos^2x+cosx-1=0

Answer 1

4cos²x(cosx-1)+(cosx-1)=0
(cosx-1)(4cos²-1)=0
(cosx-1)(2cosx-1)(2cosx+1)=0
cosx=1⇒x=2πn,n∈z
cosx=1/2⇒x=+-π/3+2πn,n∈z
cosx=-1/2⇒x=+-2π/3+2πn,n∈z