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The derivative of tan^(-1) ((sinx -cosx)...

The derivative of `tan^(-1) ((sinx -cosx)/(sinx +cosx))`, with respect to `(x)/(2)`, where `(x in(0,(pi)/(2))` is:

A

2

B

`2/3`

C

`1`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)=tan^(-1)((tan x-1)/(tan x+1))impliesf(x) =tan^(-1) tan (x- (pi)/4)) x epsilon(0,(pi)/2)impliesf(x)=x-((pi)/4)`
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