Correct Answer - D
We have, `l=int_((-pi)/(2))^((pi)/(2))log((2-sin x)/(2+sin x))dx`
Let `f(x)=log((2-sin x)/(2+sin x))`
Then, `f(-x)=log((2-sin(-x))/(2+sin(-x)))`
`=log((2+sin x)/(2-sin x))=log((2-sin x)/(2+sin x))^(-1)`
`=-log((2-sin x)/(2+sin x))=-f(x)`
Then, f(x) is an odd function.
`therefore int_(-(pi)/(2))^((pi)/(2))f(x)dx=0`
[`because` If f(x) is an odd function, then `int_(-a)^(a)f(x)dx=0`]
