Question

For the differential equation, find the general solution:

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

Answer 1

`dy/dx = (1 - cos x)/(1 + cos  x) = (1 - 1 + 2  sin^2 x/2)/(1 + 2  cos^2 x/2 - 1)`

`dy/dx = (sin^2   x/2)/(cos^2   x/2) = tan^2  x/2`

`dy = tan^2  x/2  dx`

On integrating

`int 1. dy = int tan^2  x/2  dx`

`int 1. dy = int (sec^2  x/2 - 1)  dx`

`y = 2  tan  x/2 - x + C`