A trigonometric identity derived from the Pythagorean theorem is called a Pythagorean identity.
Mathematically, the Pythagorean theorem states that
Hypotenuse^2 = Adjacent^2 + Opposite^2
Divide through by Hypotenuse^2
This gives
1 = cos^2(x) + sin^2(x)
Rewrite as:
cos^2(x) + sin^2(x) = 1
As a general rule, the above represents the basic Pythagorean identity.
Hence, the word that completes the blank is Pythagorean.
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