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