BALKAN 1987 Problem 3

In the triangle $ABC$ the following equality holds: $$\sin^{23}{\frac{A}{2}}\cos^{48}{\frac{B}{2}}=\sin^{23}{\frac{B}{2}}\cos^{48}{\frac{A}{2}}$$ Determine the value of $\frac{AC}{BC}$ .