f(x)= √3sinxcosx-(cosx)^2+1/2
= √3/2sin2x -1/2cos2x
= sin(2x-π/6)
则递减区间为
π/2 + 2kπ≤2x-π/6≤3π/2 + 2kπ
即f(x)的递减区间为
π/3+kπ≤ x ≤5π/6 +kπ