已知函数f(x)=sin(2x+派/4)+sin(2x-派/4) (1)化简并求出最小正周期.

问题描述:

已知函数f(x)=sin(2x+派/4)+sin(2x-派/4) (1)化简并求出最小正周期.

f(x)=sin(2x+π/4)+sin(2x-π/4)
=2sin(2x+π/4+2x-π/4)/2cos(2x+π/4-2x+π/4)/2
=2sin2xcosπ/4
=√2sin2x
所以最小正周期T=2π/2=π