# Pythagorean identities

## Definition

A mathematical relation of two trigonometric functions that derived from Pythagorean Theorem is called a Pythagorean trigonometric identity or simply called a Pythagorean identity.

The Pythagorean Theorem actually represents a mathematical relation between three sides of a right angled triangle in square form.

It can be transformed in ratio of any two sides of the triangle and each ratio between any sides can be represented by a trigonometric function. Likewise, it can be expressed in terms of trigonometric functions.

### List

There are three Pythagorean identities in trigonometry. Remember, all of them are written in mathematical form by assuming theta as the angle of a right angled triangle.

01

#### Relation between Sine and Cosine

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

02

#### Relation between Secant and Tangent

$\large \sec^2 \theta -\tan^2 \theta = 1$

03

#### Relation between Cosecant and Cotangent

$\large \csc^2 \theta -\cot^2 \theta = 1$