cos2x=1/2,求X等于?

题目

cos2x=1/2,求X等于?
已知cos2x=1/2,其中X的取值范围是kπ+π/2到（k+1）π,求X?我算出来是kπ+π/6,答案是kπ+5π/6.为啥呢?求详细说明,

答案

cos(2x)=1/2
2x = 2k'π ± π/3
x = k'π ± π/6
put k-1 = k'
x = (k+1)π ± π/6
x的取值范围是kπ+π/2到(k+1)π
=>x = (k+1)π - π/6 = kπ+5π/6