\( \frac{\sin x dx}{\cos x} + \frac{\cos y dy}{\sin y} = 0\)

\( \int{\frac{\sin x dx}{\cos x}} + \int{\frac{\cos y dy}{\sin y}} = \int{0} \)

\( - ln (\cos x) + ln (\sin y) = ln c\)

\( ln (\sin y) =ln (\cos x)+ ln c\)

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