Question

2a sales de I+ los ry
I-cor an​

Answer 1

$\large\rm { \frac{dy}{dx} = \frac{1+ \cos 2y}{1- \cos 2x}}$

$\large\rm{ \frac{dy}{1 + \cos 2y} = \frac{dx}{1 + \cos 2x}}$

$\large\rm { \cos 2x = 2 \cos^{2} x -1}$

$\large\rm { \cos 2y = 2 \cos^{2} y -1}$

Integrating both sides,

$\large\rm { \int \frac{dy}{2 \cos^{2} y} = \int \frac{dx}{ 2 \cos^{2} x}}$

$\large\rm { \int \sec^{2} ydy = \int \sec^{2} xdx}$

$\large\rm { \tan \ y = \tan \ x + C}$