sin^(2)(2tan^(-1)sqrt((1+x)/(1-x)))=;|x|<1

sin^(2)(2tan^(-1)sqrt((1+x)/(1-x)))="____","where "-1lexlt1

sin^(2)(2tan^(-1)sqrt((1+x)/(1-x)))="____","where "-1lexlt1

Evaluate: int sin^2(2tan^-1 sqrt((1+x)/(1-x)))dx, -1lex<1 .

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)))}

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

(iv) If y=tan^(-1)(x/(1+sqrt(1-x^(2))))+sin(2tan^(-1)sqrt((1-x)/(1+x))) , then find (dy)/(dx) for x epsilon(-1,1)

Differentiate tan^(-1)(x)/(1+sqrt((1-x^(2))))+{2tan^(-1)sqrt(((1-x)/(1+x)))}sin w.r.t.x

Prove that sin(2 tan^-1(sqrt((1+x)/(1-x))) = sqrt(1-x^2) , - le x < 1