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IIT JEE Advanced 2012 Paper 2

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Question : 55

Total: 60

For every integer n, let an and bn be real numbers. Let function
f : R → R be given by
f (x) =

an+sinπx	for‌x∊[2n,2n+1]
bn+cosπx	for‌x∊(2n−1,2n)

, for all integers n. If f is continuous, then which of the following hold(s) for all n?

an−1−bn−1 = 0
an−bn = 1
an−bn+1 = 1
an−1−bn = - 1

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