From the first judgment box, we can know that the function f(x) satisfies f(-x)=f(x), that is, the function is even; According to the second decision box, this function has two zeros.

A.f (-x) =-sinx+cosx ≠ sinx+cosx, so f(x) is not an even function;

B.f (-x) = ln (|-x |-1) = ln (| x |-1) = f (x), which is an even function; Let ln(|x|- 1)=0, then |x|- 1= 1, the solution is x = 2, that is, this function has two zeros, so it meets the conditions and is correct;

C.f (-x) = (-x) 2+|-x | = x2+| x | = f (x) is an even function, so f(x)=0, and the solution is |x|=0, that is, x=0, which does not meet the conditions, so it is incorrect;

D.f(-x)=α？ x？ αxα？ X+αx=-f(x) is not an even function.

To sum up, only B meets the requirements.

So choose B.