`If y=1/2sin^(- 1)((2x y)/(x^2+y^2))andyltxlim_(y-gt0)x= `

if y=(1)/(2)sin^(-1)((2xy)/(x^(2)+y^(2))) and y

If y=(sin^(-1)x)^2 ,prove that (1-x^2)y_2-x y_1-2=0.

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=sin^(-1)x/sqrt(1-x^(2)) show that (1-x^(2))y_(2)-3xy_(1)-y=0 .

If y=(sin^(-1)x)^2 , prove that (1-x^2)y_2-x y_1-2=0 .

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_2-3xy_1-y=0

Find the values of the following tan frac(1)(2) [sin^(-1)((2x)/(1+x^2))+ cos^(-1) ((1-y^2)/(1+y^2))],|x| lt 1, y gt 0 and x y lt 1

If y=(sin^(-1)x)^(2), prove that (1-x^(2))y_(2)-xy_(1)-2=0

If y=sin(mtan^(-1)x) , prove that : (1+x^(2))^(2)y_(2)+2x(1+x^(2))y_(1)+m^(2)y=0 .

If y=(sin^(-1)x)^2,\ then (1-x^2)y_2 is equal to x y_1+2 (b) x y_1-2 (c) x y_1+2 (d) none of these