if `y=1/2sin^-1((2xy)/(x^2+y^2))` and `y < x` then `lim_(y->0) x`

If y=(1)/(2)sin^(-1)((2xy)/(x^(2)+y^(2))) and y lt x then Lt_(y to 0)=

If y=(sin^-1x)^2/2,then(1-x^2)y_2-xy_1 =

If y=(sin^-1x)^2/2,then(1-x^2)y_2-xy_1 =

Prove that tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}=(x+y)/(1-xy) , where |x| lt 1,y gt 0 and xy lt 1 .

If y=e^(2 sin ^(-1)x) then |((x ^(2) -1) y ^('') +xy')/(y)| is equal to

If y=e^(2 sin ^(-1)x) then |((x ^(2) -1) y ^('') +xy')/(y)| is equal to

if y = sin^-1x , show that (1-x^2) y_2 = xy_1