Prove this identity:
arcsin(x-1/x+1) = 2arctan(sqrt(x)) - pi/2
First of all to prove this do i take the derivative of one side?
My book does a horrible job at explaining any of this and then they throw problems like this in there.
I tried taking the derivative of the right side and got
arcsin(x-1/x+1) = 1/[sqrt(x) + (x)sqrt(x)]
but im not sure what to do from here or even if i am doing it correctly.
any help would be great.
thank you
Perhaps he meant to write:
because that does hold when (and everywhere in fact, because it's true!).
We are going to show that
Using the sum identity, the right side becomes:
Using the double angle formula ( , with in this case), we can draw out the triangle and find:
as desired.