Hello,
in a physics exercise I need the derivative of
. I don't want not only look in my Bronstein for the derivative, I want to calculate it on my own by using the theorem of the inverse function. The tangent is in the intervall
strict monoton so that it is bijective and the inverse exists.
Now I calculate:
Now I have the problem, that I don't know how to express this in
for a clear correspondence. I looked in my mathbook and found the relation:
With this it is clear, because
according to assumption and I got:
.
Could someone explain me the relation
please? I thought about trigonometric relations like pythagoras but I did not see it.
Thanks for help