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**1. Homework Statement**

prove the identity:

arcsin( x-1/x+1 ) = 2 * arctan( sqrt(x) ) - pi/2

**2. Homework Equations**

if f'x = g'x for all x in an interval (a,b) then f - g is constant on (a,b); that is, fx = gx + c where c is constant.

this material above is in the same section as rolles thm and the mean value thm if that helps at all.

**3. The Attempt at a Solution**

Im assuming that i use arcsin(value) as fx and 2arctan(value) as gx and verify that their derivatives are equal, however i cant seem to do this. this is what i got... :

d/dx arcsin( x-1/x+1 ) = 1/( sqrt( 1 - ( x-1/x+1 )^2 ) ) * ( x+1 - x-1 / ( x+1 )^2

and

d/dx 2arctan(sqrt( x) ) = 2/(1+ sqrt(x^2)) * 1/(2 * sqrt(x)) = 2/(1+x) * 1/(2 * sqrt(x) )

my real questions here is what are the real derivatives of these two functions and can someone please right down the solution to that explicitly so i am not confused, THANK YOU PHYSICS FORUMS MEMBERS.

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**