f(x)=asin(x+Ω/4)+cos(x-Ω/4)是偶函数,
∴asin(-x+Ω/4)+cos(-x-Ω/4)=asin(x+Ω/4)+cos(x-Ω/4),
∴a[sin(x+Ω/4)-sin(-x+Ω/4)]=cos(x+Ω/4)-cos(x-Ω/4),
∴2acos(Ω/4)sinx=-2sinxsin(Ω/4)对x∈R恒成立,
∴a=-tan(Ω/4).
f(x)=asin(x+Ω/4)+cos(x-Ω/4)是偶函数,
∴asin(-x+Ω/4)+cos(-x-Ω/4)=asin(x+Ω/4)+cos(x-Ω/4),
∴a[sin(x+Ω/4)-sin(-x+Ω/4)]=cos(x+Ω/4)-cos(x-Ω/4),
∴2acos(Ω/4)sinx=-2sinxsin(Ω/4)对x∈R恒成立,
∴a=-tan(Ω/4).