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If y=tan^(-1)((sinx+cosx)/(cosx-sinx)) ,...

If `y=tan^(-1)((sinx+cosx)/(cosx-sinx))` , then `(dy)/(dx)` is equal to

A

`(1)/(2)`

B

0

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have ,
`y = tan^(-1) ((1 + tan x)/(1 - tanx)) = tan^(-1)[tan((pi)/(4) + x )] = (pi)/(4) + x `
` therefore (dy)/(dx) = 1`
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