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

Prove that (sin^(-1)x)=tan^(-1){x/(sqrt(1-x^(2)))}

If y=tan^(-1)((x)/(sqrt(1+x^(2))-1)), then (dy)/(dx)=

(tan^(-1)x)/(sqrt(1-x^(2))) withrespectto sin ^(-1)(2x sqrt(1-x^(2)))

Differentaite w.r.t x , y = tan^(-1) (x /(sqrt(1+x^(2))-1))

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

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

int_(0)^(1)tan ^(-1) (x/sqrt(1-x^(2)))dx=

The derivative of tan^(-1)((sqrt(1+x^(2))-1)/(x)) with respect to tan^(-1)((2x sqrt(1-x^(2)))/(1-2x^(2))) at x=0 is (1)/(8)(b)(1)/(4)(c)(1)/(2)(d)1