Find the general solution of each of the following differential equations:
`(dy)/(dx)=(1-cos x)/(1+cosx)`

Options

A. ` y = tan.x/2+c`
B. `y = 2 tan.x/2 +c`
C. ` y = 2 tan. x/2 -x +c`
D. ` y = 2tan. x/2 +x + c`

Answer

c

Explanation

The given equation is `(dy)/(dx) = (1-cosx)/(1+cosx)`
` rArr (dy)/(dx) = (2 sin^(2) x//2)/(2 cos^(2)x//2)`
` rArr (dy)/(dx) = tan^(2) x//2`
` rArr dy = (tan^(2)x//2) dx`
On integratng both sides , we get
` int dy = int tan^(2) x//2 dx`
` = int (sec^(2). x/2 -1)dx`
` = (tan.x/2)/(1//2)-x +c`
` rArr y = 2 tan. x/2 - x +c`