More fun in 2015, Part 15

Algebra Level 2

\[ \large \begin{cases} {a_n=a_{n-1}a_{n-2}-b_{n-1}b_{n-2} } \\ { b_n=b_{n-1}a_{n-2}+a_{n-1}b_{n-2} } \end{cases} \]

Two sequences \(a_n\) and \(b_n\) begin with values \(a_1=b_1=a_2=b_2=1\) and satisfy the recursive relations above for \(n>2\).

Find \(\large \frac{b_{2015}}{a_{2015}}\).

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