∵sin(a−

π

4

)＝

1

3

，
∴cos(a+

π

4

)=cos[（α−

π

4

）+

π

2

]
=cos（α−

π

4

）cos

π

2

-sin（α−

π

4

）sin

π

2

=-sin(a−

π

4

)=-

1

3

．
故答案为：-

1

3