the correct solution of the differential equation dy/dx = (1-cosx) / (1+cos x) is-

y = 2 tan (x/2) - x +C

The given differential equation is dy/dx = (1-cosx) / (1+cos x)

⇒ dy/dx = 2 sin²(x/2) / 2 cos²(x/2)

            =tan²(x/2)

⇒ dy/dx = sec²(x/2) -1

separating the variables, we get

dy ={ sec²(x/2) -1} dx

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

∫dy = ∫{ sec²(x/2) -1} dx

⇒ y = 2tan(x/2) - x +C

which is the solution of the given differential equation.

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