The value of k if the equation 2 cos x + cos 2kx = 3 has only one solution is

2cos⁡x+cos⁡2kx=3⇒ 21−2sin2⁡x2+1−2sin2⁡kx=3⇒ 2sin2⁡x2+sin2⁡kx=0---1Since sin2⁡x2 and  sin2⁡kx are both non-negative, Eq.(1)is possible only if sin2⁡x2=0 and  sin2⁡kx=0x=0,±2π,±4π,…But for Eq. (1) to have unique solution, the possible value of k is irrational.∴ k=2 is the possible option.