tan[(1)/(2)sin^(-1)(2a)/(1+a^(2))+(1)/(2)cos^(-1)(1-a^(2))/(1+a^(2))]

To prove that tan((1)/(2)sin^(-1)((2x)/(1+x^(2)))+(1)/(2)cos^(-1)((1-x^(2))/(1+x^(2)))=(2x)/(1-x^(2))

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

tan((1)/(2) sin ^(-1)""(2x)/(1+x^(2))+(1)/(2)cos^(-1)((1-x^(2))/(1+x^(2))))=(2x)/(1-x^(2))(|x|ne 1)

tan [(1)/(2) sin^(-1)""(2x)/(1+x^(2))+(1)/(2) cos ^(-1)""(1-y^(2))/(1+y^(2))], xy ne 1

Express the value of the following in simplest form. "tan"{1/(2)"sin"^(-1)(2x)/(1+x^(2))+1/(2)"cos"^(-1)(1-y^(2))/(1+y^(2))}

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

If x=tan ((1)/(2) sin ^(-1)((2t)/( 1+t^(2))) +(1)/(2)cos ^(-1) ((1-t^(2))/( 1+t^(2)))), then y= (2t)/( 1-t^(2)), then (dy)/(dx)=

tan[1/2sin^(-1)((2x)/(1+x^(2)))-1/2cos^(-1)((1-y^(2))/(1+y^(2)))]=