A trigonometric identity that represents Pythagorean Theorem in terms of trigonometric functions is called Pythagorean trigonometric identity or simply Pythagorean identity.
Pythagorean Theorem expresses the relation between lengths of three sides of a right angled triangle in square form.
The same theorem can be transformed in ratios of two sides of the right angled triangle and then the associated ratios can be replaced by the trigonometric functions to get the Pythagorean theorem in terms of trigonometric functions.
The six trigonometric functions can represent Pythagorean Theorem in three different forms. For example, If theta ($\theta$) is an angle of the right angled triangle, The Pythagorean theorem can be expressed in terms of trigonometric functions in the following three ways.
$\sin^2 \theta + \cos^2 \theta = 1$
The identity is read as sin squared theta plus cos squared theta is equal to one.
The relation between sine and cosine functions exactly expresses the Pythagorean Theorem. Hence, the Pythagorean relation between sine and cosine is called the fundamental Pythagorean trigonometric identity.
Learn the proof of Pythagorean relation between sine and cosine functions.
$\sec^2 \theta -\tan^2 \theta = 1$
It is read as secant squared theta minus tan squared theta is equal to one.
The relation between secant and tangent in square form also represents the Pythagoras theorem and learn the proof of Pythagorean trigonometric identity of secant and tangent.
$\csc^2 \theta -\cot^2 \theta = 1$
It is read as cosecant squared theta minus cot squared theta is equal to one.