" 1."(sin^(-1)x)^(2)-(cos^(-1)x)^(2)

Differentiate w.r.t x (i) b tan ^(-1)(x/a+tan^(-1)"(x)/a) (ii) (sin ^(-1)x)^(2)-(cos^(-1)x)^2

If [.] denotes the greatest integer function, then find the value of [sin^(-1)[x^(2)+1/2]+cos^(-1)[x^(2)-1/2]]

Suppose [x] = greatest integer le x Let f(x) = sin^(-1)[x^(2) + 1/2]-cos^(-1)[x^(2)-1/2] , Then range of f is:

The range of sin^(-1)[x^(2)+1/2] + cos^(-1)[x^(2)- 1/2] , where [.] denotes the greatest integer function, is

If quad cos^(-1)x<1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+...oo=2 then the value of 12x^(2) is

If 0ltcos^(-1)x lt 1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+…….oo=2 , then the value of 12x^(2) is

If 0 lt cos^(-1)x lt 1 and 1+sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+…infty=2 , then the value of 12x is

If 0 < cos^(-1)x < 1 and 1+ sin(cos^(-1)x)+sin^(2)(cos^(-1)x)+sin^(3)(cos^(-1)x)+.....oo=2 then x equals

The range of the function f(x)=sin^(-1)[x^(2)-(1)/(3)]-cos^(-1)[x^(2)+(2)/()] is (where, [x] represents the greatest integer value of x)