函数f(x)＝sin(x+π3)sin(x+π2)的最小正周期是T=_
问题描述：
函数f(x)＝sin(x+
)sin(x+π 3
)的最小正周期是T=______ π 2
答
y＝sin(x+
)sin(x+π 3
)＝(sinxcosπ 2
+cosxsinπ 3
)cosx=π 3
sinxcosx+1 2
cos2x＝
3
2
sin2x+1 4
•
3
2
=1+cos2x 2
+
3
4
sin(2x+1 2
)∴T=π．π 3
故填：π．