211tan^(-1)(1000x)/(1+x)=(1)/(2)sin^(2)(x)/(sqrt(1+x^(2)))

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

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

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

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)))) .

tan^(-1)sqrt((1-x)/(1+x))+sin^(-1)2x sqrt(1-x^(2))=(5 pi)/(12) if x=

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

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

If "tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))=alpha , then prove that x^(2) =sin 2alpha .

If tan^(-1)((sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))))=alpha" then prove that "x^(2)=sin2alpha.