Pythagorean identities


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

right angled triangle

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.


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.


Relation between Sine and Cosine

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


Relation between Secant and Tangent

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


Relation between Cosecant and Cotangent

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

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