求f(x)=sinx/2四次方+cosx/2四次方+四分之根号三倍sin2x最小正周期

求f(x)=sinx/2四次方+cosx/2四次方+四分之根号三倍sin2x最小正周期
求f(x)=sinx/2四次方+cosx/2四次方+四分之根号三倍sin2x最小正周期

求f(x)=sinx/2四次方+cosx/2四次方+四分之根号三倍sin2x最小正周期
=(（sin^2 (x/2) +(cos^2 (x/2))^2-2×sin^2(x/2)cos^2(x/2)+ √3/4sin2x
=1-1/2(2sin(x/2)con(x/2))^2+√3/4sin2x
=1-1/2sin^2(x)+ √3/4sin2x
=1-1/2(1/2×(1-cos2x))+√3/4sin2x
=1-1/4+1/4cos2x+√3/4sin2x
=3/4+1/2(1/2cos2x+√3/2sin2x)
=3/4+1/2(cos 60 cos 2x+sin60sin2x)=3/4+1/2cos(2(x-30))
30～30+180