For every integer n, let an and bn be real numbers. Let function f:R→R be given by
f(x)={an+sinπx,bn+cosπx,for x∈[2n,2n+1]for x∈(2n−1,2n]
for all integers n.
If f is continuous, then which of the following hold(s) for all n?
a. an−1−bn−1=0
b. an−bn=1
c. an−bn+1=1
d. an−1−bn=−1