设函数f(x)＝cos²(x+π/4)-sin²(x+π/4),x∈R,求其奇偶性和最小正周期.

设函数f(x)＝cos²(x+π/4)-sin²(x+π/4),x∈R,求其奇偶性和最小正周期.
设函数f(x)＝cos²(x+π/4)-sin²(x+π/4),x∈R,求其奇偶性和最小正周期.

设函数f(x)＝cos²(x+π/4)-sin²(x+π/4),x∈R,求其奇偶性和最小正周期.
f(x)＝cos²(x+π/4)-sin²(x+π/4)
=cos(2x+π/2)
=-sin2x,
奇函数.
T=2π/2=π.