First, recall that .
Now, from the given , you'll get .
Whan you expand , you'll get .
We can cancel an from each of the terms in the numerator and denominator and we know that and thus we have:
Since tends to zero, each of the terms with an will be zero. You'll be left with .
You made a mistake in expanding . This is not equal to because .
I hope this helps you.
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