Question

Solve
$\cos x\cdot \cos ydy-\sin x\cdot \sin ydx=0$

Answer 1

Given,

$\cos x\cos ydy-\sin x\sin ydx=0$

$\cos x\cos ydy=\sin x\sin ydx$

$\cot ydy=\tan xdx$

integrating on both sides, we get,

$\int \cot ydy=\int \tan xdx$

$\log \sin y=\log \sec x+c$