if `y= (sin ^(-1)x)/(sqrt(1-x^2))` then prove that `(1-x)^2) .d/dx=xy+1`

If y=(sin^(-1)x)/(sqrt(1-x^(2))), then ((1-x^(2))dy)/(dx) is equal to x+y (b) 1+xy1-xy(d)xy-2

Prove that (d)/(dx)(sin^(-1)x)=(1)/(sqrt(1-x^(2)) , where x in [-1,1].

If sin^(-1) x + sin^(-1) y = pi/2 , prove that x sqrt(1-x^2) + y sqrt(1-y^2) =1 .

If sin^(-1) x + sin^(-1) y = pi/2 , prove that x sqrt(1-y^2) + y sqrt(1-x^2) =1 .

If y= tan^-1 x then prove that (1+x^2) y_(2) + 2xy_(1) =0. Differentiate sec^-1(1/(2x^2 -1)) with respect to sqrt 1-x^2 .

The function y=f(x) is the solution of the differential equation (dy)/(dx)+(xy)/(x^(2)-1)=(x^(4)+2x)/(sqrt(1-x^(2))) in (-1, 1) satisfying f(0)=0 . Then underset((-sqrt(3))/(2))overset((sqrt(3))/(2))intf(x)dx is

Differentiate x^(2)+y^(2)-3xy=1

Prove the following: sin^-1x-sin^-1y = sin^-1[x(sqrt(1-y^2))-y(sqrt(1-x^2))]

The solution of the differential equation xdy+ydx-sqrt(1-x^(2)y^(2))dx=0 is (A)sin^(-1)(xy)=C-x(B)xy=sin(x+c)(C)log(1-x^(2)y^(2))=x+c(D)y=x sin x+c

Differentiate sec(x+y) = xy