[" if "x=1],[" iffe "tan^(-1)((x)/(1+sqrt(1+x^(2))))],[sin(x+ax^(-1)sqrt((1)/(1+x)))]

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

(tan^(-1)x)/(sqrt(1-x^(2))) withrespectto sin ^(-1)(2x sqrt(1-x^(2)))

(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)

prove that tan^(-1)((x)/(1+sqrt(1-x^(2)))]=(1)/(2)sin^(-1)x

Prove that tan^(-1)((x)/(1+sqrt(1-x^(2))))=(1)/(2)sin^(-1)x .

[" 0.",int sin^(-1)sqrt((x)/(a+x))dx" is equal to "],[," 1) "(x+a)tan^(-1)sqrt((x)/(a))-sqrt(ax)+C],[" 3) "(x+a)cot^(-1)sqrt((x)/(a))-sqrt(ax)+C," 2) "(x+a)tan^(-1)sqrt((x)/(a))+sqrt(ax)+C]