Pythagorean identities

A trigonometry identity, which is derived from Pythagorean Theorem is called Pythagorean identity.

Introduction

There are three possibilities to form Pythagorean identities in terms of trigonometric functions in trigonometry. They are used as formulas in trigonometry. So, it is very important to remember them to study the trigonometry.

Sine and Cosine functions

The sum of the squares of the sine and cosine functions at an angle is equal one.

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

Secant and Tangent functions

The subtraction of the square of tangent function from square of secant function at an angle 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 at an angle is equal to one.

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