Pythagorean identities

A mathematical relation between two trigonometric functions that represents the Pythagorean Theorem is called the Pythagorean identity.

Introduction

In trigonometry, there are six basic trigonometric functions but one trigonometric function with another trigonometric function can express the Pythagorean theorem mathematically. Actually, the six trigonometric ratios can possibly represent the Pythagorean theorem in three mathematical forms and they are called as the Pythagorean identities.

Now, let us learn the list of three Pythagorean identities with their proofs.

Sine and Cosine functions

The sum of the squares of the sine and cosine functions is equal to one.

$\sin^2{\theta} + \cos^2{\theta} = 1$

Secant and Tangent functions

The subtraction of the square of tan function from square of secant function is equal to one.

$\sec^2{\theta} \,-\, \tan^2{\theta} = 1$

Cosecant and Cotangent functions

The subtraction of the square of cotangent function from square of cosecant function is equal to one.

$\csc^2{\theta} \,-\, \cot^2{\theta} = 1$