Question

已知函数f(x)=2cos的平方-cos(2x 派\2)求f(派\8)的值,求函数f(x)的最小正周期及单调减区间

Answer 1

f(x)=2cos²x -cos(2x+π/2)=1+cos(2x) +sin(2x)=1+√2 sin(2x+π/4)

f(π/8)=1+√2sin(π/2)=1+√2 Tmin=2π/2=π

2kπ+π/2≤2x+π/4≤2kπ+3π/2 kπ+π/8≤x≤kπ+5π/8 区间[kπ+π/8,kπ+5π/8]