[" 48MATHEMATICS "],[" 9.tan "^(-1)(x)/(sqrt(a^(2)-x^(2))),|x|

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

int(1+tan^(2)x)/(sqrt(tan^(2)x+3))

tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

tan^(-1){sqrt((a-x)/(2+x))},-a

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

Prove that "tan"^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=pi/(4)+1/(2)"cos"^(-1)x^(2) .

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

(d)/(dx)[tan^(-1)((x-sqrt(a^(2)-x^(2)))/(x+sqrt(a^(2)-x^(2))))]=

Derivative of tan ^(-1) ((sqrt( 1+x^(2))-1)/( x)) w.r.t. tan ^(-1) ((2x sqrt(1-x^(2)))/( 1-2x ^(2))) is