Question

函数y=sin（x+π/3）sin（x+π/2）的最小正周期T是

Answer 1

方法一：
f(x)
=
cos
[π
/
2
-
(x
π
/
3)]
cos
[π
/
2
-
(x
π
/
2)]
=
cos
(π
/
6
-
x)
cos
(-x)
=
(√3
/
2
cos
x
1
/
2
sin
x)
cos
x
=
√3
/
2
(cos
x)^2
1
/
2
sin
x
cos
x
=
√3
/
4
2
(cos
x)^2
1
/
4
2
sin
x
cos
x
=
√3
/
4
[1
cos
(2
x)]
1
/
4
sin
(2
x)
=
√3
/
4
1
/
2
[√3
/
2
cos
(2
x)
1
/
2
sin
(2
x)
=
√3
/
4
1
/
2
sin
(2
x
π
/
3)
2
π
/
2
=
π
,
所以，f(x)的最小正周期是
π
。方法二：
f(x)
=
sin
(x
π
/
3)
cos
[π
/
2
-
(x
π
/
2)]
=
sin
(x
π
/
3)
cos
(-x)
=
sin
(x
π
/
3)
cos
x
=
sin
[(x
π
/
6)
π
/
6]
cos
[(x
π
/
6)
-
π
/
6]
=
[√3
/
2
sin
(x
π
/
6)
1
/
2
cos
(x
π
/
6)]
[√3
/
2
cos
(x
π
/
6)
1
/
2
sin
(x
π
/
6)]
=
3
/
4
sin
(x
π
/
6)
cos
(x
π
/
6)
√3
/
4
[cos
(x
π
/
6)]^2
√3
/
4
[sin
(x
π
/
6)]^2
1
/
4
cos
(x
π
/
6)
sin
(x
π
/
6)
=
(3
/
4
1
/
4
)
sin
(x
π
/
6)
cos
(x
π
/
6)
√3
/
4
{[cos
(x
π
/
6)]^2
[sin
(x
π
/
6)]^2}
=
1
/
2
2
sin
(x
π
/
6)
cos
(x
π
/
6)
√3
/
4
=
1
/
2
sin
(2
x
π
/
3)
√3
/
4
所以，f(x)的最小正周期是
π
。