pythagorean trigonometric identity

All these functions follow from the Pythagorean trigonometric identity.

This relation between sine and cosine sometimes is called the fundamental Pythagorean trigonometric identity.

Then use the substitution , also use the Pythagorean trigonometric identity:

The basic relationship between the sine and the cosine can also be expressed as the Pythagorean trigonometric identity:

The Pythagorean trigonometric identity then provides:

Invoking the Pythagorean trigonometric identity one obtains:

The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions.