Q 1124067851.     For every integer `n`, let `a_n` and `b_n` be real numbers.

Let function `f : RR => RR` be given by

`f(x)=a_n +sin pix` , for `x `in `[2n,2n+1]` ,

`f(x)=b_n+cos pix`, for `x` in `(2n-1,2n)`

for all integers `n.`

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

JEE 2012
A

` a_n - b_n=1`

B

`a_n-b_(n+1)=1`

C

`a_(n-1)-b_n=-1`

D

`a_(n-1) -b_(n-1) =0`

HINT

At `x=2n` and At `x=2n+1`

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