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Find the general solution of differential equation dydx=1-cosx1+cosx -

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Question

Find the general solution of differential equation `(dy)/(dx) = (1 - cosx)/(1 + cosx)`

Options

  • `2 tan  x/2 + c`

  • `2 tan  x/2 - x + c`

  • `1 - 1/c e^-x`

  • `log(e^x) + c`

MCQ

Solution

`2 tan  x/2 - x + c`

Explanation:

We have, 

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

∴ `dy = tan^2  x/2 dx`

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

∴ `y = 2 tan  x/2 - x + c`

This is the required solution.

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