Pythagorean identities
The Pythagorean identities state that
Using the unit circle definition of trigonometry, because the point is defined to be on the unit circle, it is a distance one away from the origin. Then by the distance formula, .
Another way to think of it is as follows: Suppose that there is a right triangle with the right angle at . Then, we have:
.
To derive the other two Pythagorean identities, divide by either or and substitute the respective trigonometry in place of the ratios to obtain the desired result.
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