General Solution of dy/dx = (1 - cos(x))/(1 + cos(x)):

To find the general solution of the given differential equation dy/dx = (1 - cos(x))/(1 + cos(x)), we will use separation of variables and integrate both sides.

Separation of Variables:
Separation of variables allows us to separate the variables, y and x, onto opposite sides of the equation.

dy/dx = (1 - cos(x))/(1 + cos(x))

We can rewrite the equation as:

(1 + cos(x)) dy = (1 - cos(x)) dx

Integration:
Now, we will integrate both sides of the equation with respect to their respective variables.

∫(1 + cos(x)) dy = ∫(1 - cos(x)) dx

Integrating the left side with respect to y gives us:

y + ∫cos(x) dy = x + ∫(1 - cos(x)) dx

Simplifying further:

y + ∫cos(x) dy = x + ∫dx - ∫cos(x) dx

The integral of dx is x, and the integral of cos(x) dx is sin(x):

y + y sin(x) = x + (x - sin(x))

Combining like terms:

y(1 + sin(x)) = 2x - sin(x)

Isolating y:
To find the general solution, we need to isolate y. Divide both sides of the equation by (1 + sin(x)):

y = (2x - sin(x))/(1 + sin(x))

General Solution:
Thus, the general solution of the given differential equation dy/dx = (1 - cos(x))/(1 + cos(x)) is:

y = (2x - sin(x))/(1 + sin(x))

This equation represents the family of all possible solutions to the given differential equation.