Question

函数y=[cos(x-π/12)]^2+[sin(x+π/12)]^2-1是周期为___的____(奇/偶)函数.

Answer 1

y=[cos(x-π/12)]^2+[sin(x+π/12)]^2-1

=[1+cos(2x-π/6)]/2+[1-cos(2x+π/6)]/2-1

=[cos(2x-π/6)-cos(2x+π/6)]/2

=(1/2)*(-2)sin2xsin(-π/6)

=(1/2)sin2x

所以填入：π,奇