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montana111
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Homework Statement
prove the identity:
arcsin( x-1/x+1 ) = 2 * arctan( sqrt(x) ) - pi/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.
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 can't 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.