सरलतम रूप में लिखे।
`tan^(-1)""(x)/(sqrt(a^(2)-x^(2)))`

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

the derivation of tan ^(-1)((sqrt(1+x^(2))-1)/(x)) with respect to tan^(-1)((2x sqrt(1-x^(2)))/(1-2x^(2)))

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

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

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))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=pi/4+1/2cos^(-1)x^(2) .