[" 32.Prove that "tan(1)/(2)[sin^(-1)(2x)/(1+x^(2))+cos^(-1)(1-y^(2))/(1+y^(2))]],[(x+y)/(1-xy)" if "|x|<1,y>0" and "xy<1]

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

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 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)(1/(x+y))+tan^(-1)(y/(x^2+xy+1) )= cot^(-1)x .

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

Prove that tan ^(-1)""(1)/(x+y)+ tan ^(-1)""(y)/(x^(2)+xy+1)= cot ^(-1)x.

Find the value of the following: tan1/2[sin^-1(2x/(1+x^2)) + cos^-1(1-y^2)/(1+y^2)], |x| 0 ਅਤੇ xy<1

sin^(-1)x+sin^(-1)y=cos^(-1)(sqrt(1-x^(2))sqrt(1-y^(2))-xy) if x in[0,1],y in[0,1]