Solve the following differential equation: `cosxcosy(dy)/(dx)=-sinxsiny`

Explanation

Given,
$$\cos x \cos y d y-\sin x \sin y d x=0$$
$$\cos x \cos y d y=\sin x \sin y d x$$
$$\cot y d y=\tan x d x$$
integrating on both sides, we get,
$$\int \cot y d y=\int \tan x d x$$
$$\log \sin y=\log \sec x+c$$