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`

Write the simplest form : cos^(-1)(sqrt(((sqrt(1+x^2) +1)/(2sqrt(1+x^2))))

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

Write the simplest form : tan^(-1)(1/sqrt(x^2 -1)) , |x|gt1

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

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

Write into the simplest form: cot^(-1)(sqrt(1+x^(2))+x)

Write the simplest form : cot^(-1) [(sqrt(1+sinx)+sqrt(1-sin x))/(sqrt(1+sinx)-sqrt(1-sin x)]], x epsilon [0, pi/4]

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

tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))),absxx le 1/sqrt2 , is equal to