The solution of the differential equation $cos\, x \, sin \, y dx + sin \, x \, cos \, y \, dy = 0, $ is

$sin\, x\, sin\, y = C$

The correct answer is option (4) : $sin\, x\, sin\, y = C$

$cos\, x \, sin \, y dx + sin \, x \, cos \, y \, dy = 0 $

$⇒ sin\, y\, d (sin\, x) + sin\, x \, d (sin \, y ) = 0 $

$⇒d(sin\, x \, sin \, y ) = 0 $

On integrating, we get $sin\, x \, sin\, y = C$