函数f(x)=sinx/sinx+2倍sin2分之x是以多少为周期的奇／偶函数?

求函数f(x)=sinx/[sinx+2sin(x/2)]的最小正周期,并证明f(x)是偶函数.
f(x)=[2sin(x/2)cos(x/2)]/[2sin(x/2)cos(x/2)+2sin(x/2)]
=cos(x/2)/[1+cos(x/2)]=[2cos²(x/4)-1]/[2cos²(x/4)]
=1-(1/2)sec²(x/4)=(1/2)[2-sec²(x/4)]=(1/2)[1-tan²(x/4)]
f(-x)=(1/2)[1-tan²(-x/4)]=(1/2)[1-tan²(x/4)]=f(x),故是偶函数.
最小正周期T=π/(1/4)=4π