函数f(x)＝sin(x+π3)sin(x+π2)

y＝sin(x+
π
3)sin(x+
π
2)＝(sinxcos
π
3+cosxsin
π
3)cosx=
1
2sinxcosx+

3
2cos2x＝
1
4sin2x+

3
2•
1+cos2x
2=

3
4+
1
2sin(2x+
π
3)∴T=π．
故填：π．