Please solve cot^2x - csc^2x =

cot(x) is defined as adjacent / opposite.
csc(x) is defined as hypotenuse / opposite
So csc^2(x) - cot^2(x) = (hyp^2 - adj^2) / opp^2.
By the pythagorean theorem, (hyp^2 - adj^2) = opp^2
therefore, csc^2(x) - cot^2(x) = 1
Therefore, -csc^2(x) + cot^2(x) = -1
Q.E.D.