函数y=cos^2(x+派/4)-sin^2(x+派/4)的最小正周期

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函数y=cos^2(x+派/4)-sin^2(x+派/4)的最小正周期

函数y=cos^2(x+派/4)-sin^2(x+派/4)的最小正周期
函数y=cos^2(x+派/4)-sin^2(x+派/4)的最小正周期

函数y=cos^2(x+派/4)-sin^2(x+派/4)的最小正周期
y=2cos(x π/4)*cos(x-π/4) (√3)sin2x =2sin(π/4-x)*cos(π/4-x) (√3)sin2x =sin(π/2-2x) (√3)sin2x =cos2x (√3)sin2x =2[cosπ/3cos2x sinπ/3sin2x] =2cos(2x-π/3) 所以,值域[-2,2],周期为π,2kπ