`tan^(- 1)x=sin^(-1)\ x/(sqrt(1+x^2))`

int(tan(cos^(-1)x)+cot(sin^(-1)x))/(sqrt(1-x^(2)))dx=

Prove that tan (sin^(-1)x) = x/(sqrt(1-x^(2))) - 1 lt x lt 1 .

Prove the following: tan^-1x = sin^-1(frac{x}{sqrt(1+x^2)})

int (tan (sin^(-1)x))/(sqrt(1-x^(2)))dx=

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

Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))="sin"^(-1)((y-x)/(sqrt(1+x^(2))sqrt(1+y^(2)))) .

Prove that tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt(1+x^(2))*sqrt(1+y^(2))))

solve : tan^(-1) sqrt(x(x+1))+sin ^(-1) (sqrt(1+x+x^(2)))=(pi)/(2)

int(sin^(2)x*sec^(2)x+2tan x*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx