ज्ञात करें `int(1+sinx)/(1-sinx)dx`

Explanation

`(1+sinx)/(1-sinx)=((1+sinx)(1+sinx))/((1-sinx)(1+sinx))`
`=((1+sinx)^2)/(1-sin^2x)=(1+2sinx+sin^2x)/(cos^2x)=1/(cos^2x)+(2sinx)/(cos^2x)+(sin^2x)/(cos^2x)`
`=sec^2x+2tanx ecx+tan^2x`
`=sec^2x+2tanxsecx+(sec^2x-1)`
`=2sec^2x+2tansecx-1`
`:." "int(1+sinx)/(1-sinx)dx=int(2sec^2x+2secxtanx-1)dx`
`=2intsec^2xdx+2intsec x tan x dx - dx`
`=2 tan x +2sec x - x +c`