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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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