f(-x)=asin(-2x+π/4)+cos(-2x+π/4)
=asin(-2x)cosπ/4+acos(-2x)sinπ/4+cos(-2x)cosπ/4-sin(-2x)sinπ/4
=-asin2xcosπ/4+acos2xsinπ/4+cos2xcosπ/4+sin2xsinπ/4,
f(x)=asin(2x+π/4)+cos(2x+π/4)
=asin2xcosπ/4+acos2xsinπ/4+cos2xcosπ/4-sin2xsinπ/4,
由偶函数的性质f(-x)=f(x),得：
2asin2xcosπ/4=2sin2xsinπ/4,
——》a=1.