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(d)/(dx)sqrt((1-sin2x)/(1+sin2x)) is equ...

`(d)/(dx)sqrt((1-sin2x)/(1+sin2x))` is equal to, `(0ltxltpi//4),`

A

`sec^(2)x`

B

`-sec^(2)((pi)/(4)-x)`

C

`sec^(2)((pi)/(4)+x)`

D

`sec^(2)((pi)/(4)-x)`

Text Solution

Verified by Experts

`y=sqrt((1-sin 2x)/(1+ sin 2x))=(cos x - sin x)/(cos x + sin x)=(1-tan x)/(1+ tan x)=tan ((pi)/(4)-x)`
`therefore (dy)/(dx)=-sec^(2)((pi)/(4)-x)`
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