`int 1/(1+cosx) dx=`

Options

A. `-cot x + cosec x + C`
B. `cot x - cosec x + C`
C. `cot x + cosec x + C`
D. none of these

Answer

A

Explanation

`I = int{(1)/((1+cosx)) xx ((1-cosx))/((1-cosx))} dx = int((1-cosx))/(sin^(2)x) dx`
`= {(-1)/(sin^(2)x) - (cosx)/(sin^(2)x)} dx = int(cosec^(2)x - cosec x cot x ) dx`.