" (x) "sin{2tan^(-1)sqrt((1-x)/(1+x))}

Write each of the following in the simplest form: (i) sin^(-1){(sqrt(1+x)+sqrt(1-x))/2},\ \ 0 < x <1 (ii) sin{2tan^(-1)(sqrt((1-x)/(1+x)))}

int_(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

int_(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

Prove that sin[2tan^(-1){sqrt((1-x)/(1+x))}]=sqrt(1-x^2)

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}], find (dy)/(dx)