Which of the following is a Pythagorean Trig Identity?

The identity that is recognized as a Pythagorean Trig Identity is the equation in the correct choice: cos²θ + sin²θ = 1. This identity is fundamental in trigonometry as it relates the squares of the sine and cosine functions for any angle θ.

This relationship emerges from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In the trigonometric context, when considering a unit circle, the coordinates of a point on the circle are (cosθ, sinθ), and thus, the length of the hypotenuse is 1. Therefore, applying this theorem results in the derived identity cos²θ + sin²θ = 1.

Other options do not represent Pythagorean identities. For example, the equation sin²θ + cos²θ = 2 is incorrect since for any real angle θ, the maximum values of sin²θ and cos²θ are 1, making their sum at most 1, not 2. The identity tan²θ + 1 = cot²θ is not true universally. Instead, the