[" Consider,"f(x)=sin^(-1)sqrt(1-sqrt(x))+tan^(-1)(sqrt((1)/(sqrt(x))-1))" .If "s" is is the stofintegers in the mageof "f(x)" and "],[A=[a_(y),b_(y)" is amatrix where "a_(y)in S" and all "a_(y)" aredistinct the number of different talles "]

Consider, f(x)=sin^(- 1)sqrt(1-sqrt(x)) + tan^(- 1)(sqrt(1/(sqrt(x))-1)) If S is the set of integers in the range of f(x) and A = [a_(ij)]_(2xx2) is a matrix where a_(ij) sub S and all a_(ij) are distinct then find the no of different values of det(A).

if y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)] then prove that (1)/(2sqrt(x)sqrt(1-x))

If y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(dy)/(dx)

Consider E=(8sqrt(x)+5sqrt(y))^(y)=1+f,0<=f<1

If tan^(-1)x+cos^(-1)((y)/(sqrt(1+y^(2))))=sin^(-1)((3)/(sqrt(10))) , then

If y=(tan^(-1)(sqrt(1+sin x)+sqrt(1-sin x)))/(sqrt(1+sin x)-sqrt(1-sin x)) find the value of (dy)/(dx)

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