Which of the following options is a Pythagorean Identity

None of them really, but C is equivalent to the Triognometric Pythagorean Theorem:
[tex](\sin x + \cos x)^2 = 1 + 2 \sin x \cos x[/tex]
[tex] \sin^2 x + 2 \sin x \cos x + \cos ^2 x = 1 + 2 \sin x \cos x[/tex]
[tex] \sin^2x + \cos ^2x = 1[/tex]
That's the Trigonometric Pythagorean Theorem
Answer: C