求y=sin(2x+π/4)+cos(2x-π/4)的最小正周期

问题描述:

求y=sin(2x+π/4)+cos(2x-π/4)的最小正周期

y=sin(2x+π/4)+cos(2x-π/4)
=sin(2x+π/4)+cos[(2x+π/4)-π/2]
=sin(2x+π/4)+sin(2x+π/4)
=2sin(2x+π/4)
∴ 最小正周期T=2π/2=π