已知函数f(x)=sin(x+π/3)sin(x+π/2)的最小正周期T=?

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已知函数f(x)=sin(x+π/3)sin(x+π/2)的最小正周期T=?
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已知函数f(x)=sin(x+π/3)sin(x+π/2)的最小正周期T=?
已知函数f(x)=sin(x+π/3)sin(x+π/2)的最小正周期T=?

已知函数f(x)=sin(x+π/3)sin(x+π/2)的最小正周期T=?
f(x)=sin(x+π/3)sin(x+π/2)
=(sinxcosπ/3+cosxsinπ/3)*cosx
=1/4sin2x+√3/4(cos2x-1)
=1/2(1/2sin2x+√3/2cos2x)-3/4
=1/2sin(2x+π/3)-3/4
最小正周期T=2π/2=π