How does 1 plus cot squared x equals csc squared x?

The proof of this trig identity relies on the pythagorean trig identity, the most famous trig identity of all time: sin2x + cos2x = 1, or 1 - cos2x = sin2x.

1 + cot2x = csc2x

1 = csc2x - cot2x

1 = 1/sin2x - cos2x/sin2x

1 = (1 - cos2x)/sin2x ...using the pythagorean trig identity...

1 = sin2x/sin2x

1 = 1

So this is less of a proof and more of a verification.