函数y=cos^(x-π/12)+sin^2(x+π/12)-1的最小正周期为( )

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函数y=cos^(x-π/12)+sin^2(x+π/12)-1的最小正周期为( )
函数y=cos^(x-π/12)+sin^2(x+π/12)-1的最小正周期为( )

函数y=cos^(x-π/12)+sin^2(x+π/12)-1的最小正周期为( )
y=cos²(x-π/12)+sin²(x+π/12)-1
=½[1+cos(2x-π/6)]+½[1-cos(2x+π/6)]-1
=½[cos(2x-π/6)-cos(2x+π/6)]
=-½ * 2 sin[(2x-π/6+2x+π/6)/2] sin[(2x-π/6-2x-π/6)/2]
=sin2x sin(π/6)
=½sin2x
=½sin(2x+2kπ)
=½sin2(x+kπ) k为整数
最小正周期为π