1.

`int ((1+ sinx))/((1- sinx)) dx=?`A. `2tanx+x-2secx+C`B. `2tanx-x+2secx+C`C. `2tanx-x-2secx+C`D. none of these

Answer» Correct Answer - B
`I=int((1+sinx))/((1-sinx))xx((1+sinx))/((a+sinx))dx`.
`=int((1+sinx)^(2))/((1-sin^(2)x))dx=int(1+sin^(2)x+2sinx)/(cos^(2)x)dx`
`=int{(1)/(cos^(2)x)+(sin^(2)x)/(cos^(2)x)+(2sinx)/(cos^(2)x)}dx`
`int(sec^(2)x+tan^(2)x+2secxtanx)dx`
`int(2sec^(2)x-1+2secxtanx)dx=tanx-x+2secx+C`.


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