If |cos x|^{2x - 3/2 sinx + 1/2} = 1, then possible values of x are ​

Question

If \(|cos x|^{sin^2x -\frac32sinx+ \frac12} = 1\) , then possible values of x are 

a. \(n\pi \;or\;n\pi + (-1)^n \frac \pi6, n\in I\)

b. \(n\pi \;or\;2n\pi + \frac \pi2\; or\;n\pi+ (-1)^n \frac \pi6, n\in I\)

c. \(\;n\pi + (-1)^n \frac \pi6, n\in I\)

d. \(n\pi, n\in I\)

Answer 1

Correct option is b. \(n\pi \;or\;2n\pi + \frac \pi2\; or\;n\pi+ (-1)^n \frac \pi6, n\in I\)