How do you verify #(1+tan^2x)/(1+cot^2x) = (tan^2x)^2#?
These are called the Trigonometric Pythagorean Identities
Suppose you have a right triangle, with sides
The first identity comes from dividing the equation by
Now, with those identities, we can substitute in the original expression:
I believe the last three parts of the equalities are well known facts, or at least extremely easy to show, hence I'll stop here with the proof.