If y = ^ - 1 (( x + x)/( x - x)), ~then (dy)/(dx) is equal to

We have,

$y = \tan^{- 1} \left(\dfrac{\sin x + \cos x}{\cos x - \sin x}\right)$

$⇒ y = \tan^{- 1} \left(\dfrac{1 + \tan x}{1 - \tan x}\right)$

⇒ y = \tan^{- 1} \left[\tan \left(\dfrac{π}{4} +x\right)\right]

$⇒ y =$\dfrac{π}{4} +$x$

Differentiating both sides w.r.t.~$x$, we get

\dfrac{dy}{dx} =$1$