Simplify `tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))` , `-1/sqrt2 lt x lt 1`

Write the simplest form : tan^(-1)( (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x) + sqrt(1-x))); (-1)/sqrt(2) le x le 1

Simplify tan^(-1)((sqrt(1+x^2)-1)/x)

The derivative of tan^(-1)((sqrt(1 + x)-sqrt(1-x))/(sqrt(1 + x)+sqrt(1-x))) is

If y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))), find (dy)/(dx)

Simplest form of tan^(-1)((sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))), pi lt x lt (3 pi)/(2) is:

Simplify :sin[2tan^(-1)sqrt((1-x)/(1+x))]

tan^-1 (sqrt(x)+sqrt(a))/(1-sqrt(x)sqrt(a))

Simplest form of tan^(-1)((sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))), pi lt x lt (3pi)/2 is :