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

$\sin x \sin y=C$

The correct answer is Option (4) → $\sin x \sin y=C$

$\cos x \sin y d x=-\sin x \cos y d y=0$

$\frac{dy}{dx}=\frac{\cos x \sin y}{-\sin x \cos y}$

$\frac{dy}{dx}=-\frac{\tan x}{\tan y}$

$\int\frac{1}{\tan y}dy=\int\frac{1}{\tan x}dx$

$\ln(|\sin x|) + \ln(|\sin y|) = C$

$\ln(|\sin x \sin y|) = C$

$\sin x \sin y = C$