The number of solutions of 12cos3⁡x−7cos2⁡x+4cos⁡x=9 is

The given equation is (cos⁡x−1)12cos2⁡x+5cos⁡x+9=0⇒cos⁡x=1 only as the other factor gives imaginary roots⇒ x=2nπ,n∈ZHence, it has infinite solutions as n∈Z