What are the Pythagorean identities?

There are three of them. Granted this means that there are different variations of all three. I'll show you the variations as well. This is coming straight from my Math 1060 (Trigonometry) notebook. Sorry there is no key to represent the angle; Theta.

1. Sin2 (of Theta) + Cos2 (of Theta)= 1

Variations: Sin2 (of Theta) = 1- Cos2 (of Theta)

AND: Cos2 (of Theta) = 1-Sin2 (of Theta)

2. Tan2 (of Theta) + 1 = sec2 (of Theta)

Variations: Tan2 (of Theta) = Sec2 (of Theta) -1

3. 1 + Cot2 (of Theta) = Csc2 (of Theta)

Variations: Cot2 (of Theta) = Csc2 (of Theta) -1