`sqrt(1+2sqrt(1+2sqrt(1+2sqrt(1+....))))=`

Find the value of sqrt((1)/(2)sqrt((1)/(2)sqrt((1)/(2)sqrt((1)/(2)......cdots oo))))

If y=tan^-1frac{sqrt(1+x^2)+sqrt(1-x^2)}{sqrt(1+x^2)-sqrt(1-x^2)] , show that x^2=sin 2y

y=tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))

If (sqrt(1 +x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))=3 then x=

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

If y = tan^(-1) ((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) show that (dy)/(dx) = x/sqrt(1-x^4) .

Prove that tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))]=pi/4+1/2cos^(-1)x^2

Prove that tan ^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))=pi/4+1/2 cos ^(-1) x^2

If y=tan^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))), x^2 le 1 , then find (dy)/(dx)

Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))} with respect to cos^(-1)x^2