Question

Find the derivatives of the following:

`tan^-1 ((cos x + sin x)/(cos x - sin x))`

Answer 1

Let y = `tan^-1 ((cos x + sin x)/(cos x - sin x))`

y = `tan^-1 ((cos x(1 + (sinx)/(cosx)))/(cos x(1 - (sin x)/(cos x))))`

y =  `tan^-1 ((1 + tanx)/(1 - tanx))`

= `tan^-1 ((tan  pi/4 + tan x)/(1 - tan  pi/4 * tan x))`

= `tan^-1 (tan (pi/4 + x))`

y = `pi/4 + x`

`("d"y)/("d"x)` = 0 + 1

`("d"y)/("d"x)` = 1