find `int(dx)/(1+sinx)`

Explanation

`int(dx)/(1+sinx)=int(dx)/(1+cos(pi//2-x))`
`=int(dx)/(2cos^(2)(pi//4-x//2))`
`=(1)/(2)int sec^(2)((pi)/(4)-(x)/(2))dx`
`=(1)/(2)(tan(pi//4-x//2))/(-(1)/(2))+c`
`=tan((x)/(2)-(pi)/(4))+c`
Given `int(dx)/(1+sinx)=tan((x)/(2)+a)+b`
or `tan((x)/(2)-(pi)/(4))+c=tan((x)/(2)+a)+b`
` :. a= -(pi)/(4)` and `b=c=` an arbitrary constant