In right angle triangles there is one 90 degree angle and two other angles that are said to be complementary angles on the basis that the sum of interior angles of a triangle is 180 degrees.
Since the two angles A and B are complementary angles they have special properties that allow us to manipulate certain trigonometric identities for right angle triangles. I originally noticed this while I was looking at compound angle formulas and realized that if the angles are complementary then it results in the co-function identities. I then appplied this theory to the Pythagorean identities and proved a new identity for right angle triangles.
The pythagorean identity states that:
In a right angle triangle this translates to: