\(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\)

x is obtuse i.e sin x = + ve while cos x = + ve

\(cos x=\frac{3}{5}==>cos x=-\frac {3}{5}(obtuse)\)

\(sin y= \frac{5}{13}\)

\(sin (x-y) = sin x\) \(cos y - cos x\) \(sin y\)

\(sin(x-y) = \frac{4}{5}\times\frac{12}{13}-(-\frac{3}{5})\times\frac{5}{13}\)

\(sin(x-y) = \frac{48}{65}-(-\frac{3}{13})\)

\(\therefore sin (x-y) = \frac{48}{65} + \frac{3}{13} = \frac{63}{65}\)