求函数y=sin(x+pai/3)sin(x+pai/2)的周期.

y=sin(x+π/3)sin(x+π/2)
=sin(x+π/3)cosx
=(sinxcosπ/3+cosxsinπ/3)cosx
=1/2sinxcosx+√3/2cos^2(x)[cos^2(x)指cosx的平方)
=1/2(1/2sin2x+√3/2cos2x)+√3/4
=1/2(2x+π/3)+√3/4
所以最小正周期T=2π/w=2π/2=π