Question

Solve :

$\frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}$

Answer 1

$\frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}$

$\frac{dy}{dx}=\frac{2si{n}^2\frac{x}{2}}{2co{s}^2\frac{x}{2}}=ta{n}^2\frac{x}{2}$

$\frac{dy}{dx}=se{c}^2\frac{x}{2}-1$

$dy=(se{c}^2\frac{x}{2}-1)dx$

Now, integrating both sides of the equation, we get,

$\int dy=\int (se{c}^2\frac{x}{2}-1)dx$

$\int dy=\int se{c}^2\frac{x}{2}dx-\int dx$

$y=2tan\frac{x}{2}-x+C$