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.
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: