Question

函數(shù)f(x)=sin2(x+

π

4

)+cos2(x-

π

4

)-1是（　�。�

A．周期為π的奇函數(shù)	B．周期為π的偶函數(shù)
C．周期為2π的奇函數(shù)	D．周期為2π的偶函數(shù)

Answer 1

f(x)=sin2(x+

π

4

)+cos2(x+

π

4

-

π

2

)-1=2sin2(x+

π

4

)-1=-cos(2x+

π

2

)
=sin2x，
所以T=

2π

2

=π，
故選A．