For -(pi)/(2)lt xlt(3pi)/(2), the value ...

For `-(pi)/(2)lt xlt(3pi)/(2)`, the value of `(d)/(dx){tan^(-1)""(cosx)/(1+sinx)}` is equal to-

A

`(1)/(2)`

B

`-(1)/(2)`

C

1

D

`(sinx)/((1+sinx)^(2))`

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