Find the value of: `tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)(1-y^2)/(1+y^2)],|x|<1, y >0` and `x y" "<" "1`

Find the value of: tan((1)/(2)[(sin^(-1)(2x))/(1+x^(2))+(cos^(-1)(1-y^(2)))/(1+y^(2))]),|x| 0 and xy,|x| 0

Find the value of tan { 1/2 sin^(-1) ((2x)/(1+x^(2))) + 1/2 cos^(-1) ((1-y^(2))/(1+ y^(2)))}

Find the value of the following: tan((1)/(2))[sin^(-1)((2x)/(1+x^(2)))+cos^(-1)((1-y^(2))/(1+y^(2)))],|x| 0 and xy<1

Prove that : tan(1/2){sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))}=(x+y)/(1-x y) , if |x| 0 and x y<1 .

Simplity tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)(1-y^(2))/(1+y^(2))} , if xgtygt1 .

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))

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)((1-x^(2))/(1+x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2))) find (dy)/(dx)

Find the value of ( 1/x + 1/y ) ( 1/x - 1/y ) ( 1/x^2 + 1/y^2 )