已知函数f(x)=1-2sin^2(x+π/4)+2sin(x+π/4)cos(x+π/4)(1)函数f(x)的最小正周期；（2)_数学解答

已知函数f(x)=1-2sin^2(x+π/4)+2sin(x+π/4)cos(x+π/4)
(1)函数f(x)的最小正周期；（2)函数f(x)的单调增区间；（3）函数f(x)在[-3π/8,π/8]的值域

人气：429 ℃　时间：2019-09-17 13:41:53

解答

f(x)=1-2sin^2(x+π/4)+2sin(x+π/4)cos(x+π/4)=cos(2x+π/2)+sin(2x+π/2)=√2[√2/2cos(2x+π/2)+√2/2sin(2x+π/2)]=√2[sin(2x+π/2+π/4)]=√2sin(2x+3π/4)(1) 最小正周期为T=2π/ω=2π/2=π(2) 函数的单调...